(x+6)(3x-1)+x+6=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x + 6)(3x - 1) + x + 6 = 0

This article will guide you through solving the equation (x + 6)(3x - 1) + x + 6 = 0. We will break down the steps and use algebraic manipulations to find the solution(s).

Step 1: Factor out the common factor

Notice that both terms in the equation share the factor (x + 6). Let's factor it out:

(x + 6)(3x - 1) + (x + 6) = 0 (x + 6)[(3x - 1) + 1] = 0

Step 2: Simplify the expression

Simplifying the expression inside the brackets:

(x + 6)(3x) = 0

Step 3: Apply the Zero Product Property

The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we have two possible solutions:

• x + 6 = 0
• 3x = 0

Step 4: Solve for x

Solving each equation:

• x = -6
• x = 0

Solution

Therefore, the solutions to the equation (x + 6)(3x - 1) + x + 6 = 0 are x = -6 and x = 0.