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Simplifying -6(x + 3)(x + 2) = 0 Reorder the terms: -6(3 + x)(x + 2) = 0 Reorder the terms: -6(3 + x)(2 + x) = 0 Multiply (3 + x) * (2 + x) -6(3(2 + x) + x(2 + x)) = 0 -6((2 * 3 + x * 3) + x(2 + x)) = 0 -6((6 + 3x) + x(2 + x)) = 0 -6(6 + 3x + (2 * x + x * x)) = 0 -6(6 + 3x + (2x + x2)) = 0 Combine like terms: 3x + 2x = 5x -6(6 + 5x + x2) = 0 (6 * -6 + 5x * -6 + x2 * -6) = 0 (-36 + -30x + -6x2) = 0 Solving -36 + -30x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-6'. -6(6 + 5x + x2) = 0 Factor a trinomial. -6((3 + x)(2 + x)) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-3, -2}
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