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Simplifying 2(2x + -3) + 12 + 2x + x2 = 78 Reorder the terms: 2(-3 + 2x) + 12 + 2x + x2 = 78 (-3 * 2 + 2x * 2) + 12 + 2x + x2 = 78 (-6 + 4x) + 12 + 2x + x2 = 78 Reorder the terms: -6 + 12 + 4x + 2x + x2 = 78 Combine like terms: -6 + 12 = 6 6 + 4x + 2x + x2 = 78 Combine like terms: 4x + 2x = 6x 6 + 6x + x2 = 78 Solving 6 + 6x + x2 = 78 Solving for variable 'x'. Reorder the terms: 6 + -78 + 6x + x2 = 78 + -78 Combine like terms: 6 + -78 = -72 -72 + 6x + x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -72 + 6x + x2 = 0 Factor a trinomial. (-12 + -1x)(6 + -1x) = 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 + -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 = {-12, 6}
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