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When solving equations, our goal is to find the value(s) of the variable that make the equation true. Equations are mathematical statements that show the equality of two expressions. By manipulating the equation, we can isolate the variable and determine its value.
One effective method, especially when dealing with polynomial equations, is to factor the expression. In the given exercise \((b-9)(b+8)=0\), the factors are already provided, simplifying the process. Solving the equation involves working with these factors.
By using properties like the zero-product property, a crucial technique explained below, solving these kinds of algebraic equations becomes systematic and straightforward.

Algebraic equations are a fundamental part of mathematics, forming the basis for algebra. They involve variables, constants, and arithmetic operations such as addition, subtraction, multiplication, and division.
These equations can be linear, quadratic, or of higher degrees, depending on the highest power of the variable present. The exercise \((b-9)(b+8)=0\)is an example of a quadratic equation, which can often be factored into simpler linear expressions.

• In quadratic equations, the solution may involve finding two or more values for the variable that meet the criteria set by the equation.
• Understanding how to manipulate and solve these equations is essential in algebra.

As you delve deeper into algebra, becoming comfortable with these equations will open doors to more complex mathematical concepts.

Factoring is a technique used to simplify equations and find solutions. It involves rewriting an expression as a product of its factors. The factors, when multiplied together, produce the original equation.
In our example, the equation \((b-9)(b+8)=0\)is already factored, with \((b-9)\) and \((b+8)\) being the factors.
To solve the equation using the zero-product property, we recognize that if the product of two factors is zero, at least one of the factors must be zero. This property is essential in finding precise solutions for equations that are factored.

• For \((b-9)\), setting it to zero gives the equation \(b-9=0\), which simplifies to \(b=9\).
• For \((b+8)\), setting it to zero gives the equation \(b+8=0\), which simplifies to \(b=-8\).

Once familiar with factoring, you can tackle complex problems with greater ease, as it is a fundamental skill that aids in simplifying and solving various algebraic equations.