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Simplifying x(x + 1) = 2x(x + -6) Reorder the terms: x(1 + x) = 2x(x + -6) (1 * x + x * x) = 2x(x + -6) (1x + x2) = 2x(x + -6) Reorder the terms: 1x + x2 = 2x(-6 + x) 1x + x2 = (-6 * 2x + x * 2x) 1x + x2 = (-12x + 2x2) Solving 1x + x2 = -12x + 2x2 Solving for variable 'x'. Reorder the terms: 1x + 12x + x2 + -2x2 = -12x + 2x2 + 12x + -2x2 Combine like terms: 1x + 12x = 13x 13x + x2 + -2x2 = -12x + 2x2 + 12x + -2x2 Combine like terms: x2 + -2x2 = -1x2 13x + -1x2 = -12x + 2x2 + 12x + -2x2 Reorder the terms: 13x + -1x2 = -12x + 12x + 2x2 + -2x2 Combine like terms: -12x + 12x = 0 13x + -1x2 = 0 + 2x2 + -2x2 13x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 13x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(13 + -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 '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {0, 13}
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