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Simplifying -6(x + 6)(x + 7) = 0 Reorder the terms: -6(6 + x)(x + 7) = 0 Reorder the terms: -6(6 + x)(7 + x) = 0 Multiply (6 + x) * (7 + x) -6(6(7 + x) + x(7 + x)) = 0 -6((7 * 6 + x * 6) + x(7 + x)) = 0 -6((42 + 6x) + x(7 + x)) = 0 -6(42 + 6x + (7 * x + x * x)) = 0 -6(42 + 6x + (7x + x2)) = 0 Combine like terms: 6x + 7x = 13x -6(42 + 13x + x2) = 0 (42 * -6 + 13x * -6 + x2 * -6) = 0 (-252 + -78x + -6x2) = 0 Solving -252 + -78x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-6'. -6(42 + 13x + x2) = 0 Factor a trinomial. -6((7 + x)(6 + x)) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {-7, -6}
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