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(2 X-1)(x+6)=0

2 min read Jun 16, 2024
(2 X-1)(x+6)=0

Solving the Equation: (2x-1)(x+6)=0

This equation is a quadratic equation in factored form. Let's break down how to solve it:

Understanding the Zero Product Property

The Zero Product Property states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero.

In our equation, we have two factors: (2x-1) and (x+6). To make the entire product equal to zero, we need at least one of these factors to be zero.

Solving for x

Let's set each factor equal to zero and solve for x:

1. Factor 1: (2x-1) = 0

  • Add 1 to both sides: 2x = 1
  • Divide both sides by 2: x = 1/2

2. Factor 2: (x+6) = 0

  • Subtract 6 from both sides: x = -6

Solutions

Therefore, the solutions to the equation (2x-1)(x+6) = 0 are:

  • x = 1/2
  • x = -6

These are the values of x that make the equation true.

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