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Chapter 5: Problem 7

Solve. $$(2 x-5)(3 x+6)=0$$

Short Answer

Expert verified
The solutions to the equation are \(x = 2.5\) and \(x = -2\).

Step by step solution

01

Identify the binomials

The equation in question is \((2x - 5)(3x + 6) = 0\). Here, \(2x - 5\) and \(3x + 6\) are the binomials. The zero product property states that if the product of two values equals 0, then at least one of the values must be 0.
02

Set each binomial equal to zero

Next step is to set each binomial equal to zero. Doing so, we have two equations to solve: \(2x - 5 = 0\) and \(3x + 6 = 0\).
03

Solve each equation

Solve the first equation \(2x - 5 = 0\), by adding 5 to both sides and dividing by 2. The solution will be \(x = 2.5\). Solve the second equation \(3x + 6 = 0\), by subtracting 6 from both sides and dividing by 3, which results in \(x = -2\).

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