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Simplifying x(x + 6)(x + -7) = 0 Reorder the terms: x(6 + x)(x + -7) = 0 Reorder the terms: x(6 + x)(-7 + x) = 0 Multiply (6 + x) * (-7 + x) x(6(-7 + x) + x(-7 + x)) = 0 x((-7 * 6 + x * 6) + x(-7 + x)) = 0 x((-42 + 6x) + x(-7 + x)) = 0 x(-42 + 6x + (-7 * x + x * x)) = 0 x(-42 + 6x + (-7x + x2)) = 0 Combine like terms: 6x + -7x = -1x x(-42 + -1x + x2) = 0 (-42 * x + -1x * x + x2 * x) = 0 (-42x + -1x2 + x3) = 0 Solving -42x + -1x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-42 + -1x + x2) = 0 Factor a trinomial. x((-6 + -1x)(7 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 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 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {0, -6, 7}
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