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Simplifying 12(6 + x) = x(6 + x) (6 * 12 + x * 12) = x(6 + x) (72 + 12x) = x(6 + x) 72 + 12x = (6 * x + x * x) 72 + 12x = (6x + x2) Solving 72 + 12x = 6x + x2 Solving for variable 'x'. Combine like terms: 12x + -6x = 6x 72 + 6x + -1x2 = 6x + x2 + -6x + -1x2 Reorder the terms: 72 + 6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 72 + 6x + -1x2 = 0 + x2 + -1x2 72 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 72 + 6x + -1x2 = 0 Factor a trinomial. (12 + -1x)(6 + x) = 0Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Subproblem 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 = {12, -6}
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