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Simplifying -6x(6 + -1x)(x + 1) = 0 Reorder the terms: -6x(6 + -1x)(1 + x) = 0 Multiply (6 + -1x) * (1 + x) -6x(6(1 + x) + -1x * (1 + x)) = 0 -6x((1 * 6 + x * 6) + -1x * (1 + x)) = 0 -6x((6 + 6x) + -1x * (1 + x)) = 0 -6x(6 + 6x + (1 * -1x + x * -1x)) = 0 -6x(6 + 6x + (-1x + -1x2)) = 0 Combine like terms: 6x + -1x = 5x -6x(6 + 5x + -1x2) = 0 (6 * -6x + 5x * -6x + -1x2 * -6x) = 0 (-36x + -30x2 + 6x3) = 0 Solving -36x + -30x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x'. 6x(-6 + -5x + x2) = 0 Factor a trinomial. 6x((-1 + -1x)(6 + -1x)) = 0 Ignore the factor 6.Subproblem 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 '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 3
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 = 6Solution
x = {0, -1, 6}
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