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Simplifying 5x2(2x + 5) + -6x = 2x2(5x + 12) + 72 Reorder the terms: 5x2(5 + 2x) + -6x = 2x2(5x + 12) + 72 (5 * 5x2 + 2x * 5x2) + -6x = 2x2(5x + 12) + 72 (25x2 + 10x3) + -6x = 2x2(5x + 12) + 72 Reorder the terms: -6x + 25x2 + 10x3 = 2x2(5x + 12) + 72 Reorder the terms: -6x + 25x2 + 10x3 = 2x2(12 + 5x) + 72 -6x + 25x2 + 10x3 = (12 * 2x2 + 5x * 2x2) + 72 -6x + 25x2 + 10x3 = (24x2 + 10x3) + 72 Reorder the terms: -6x + 25x2 + 10x3 = 72 + 24x2 + 10x3 Add '-10x3' to each side of the equation. -6x + 25x2 + 10x3 + -10x3 = 72 + 24x2 + 10x3 + -10x3 Combine like terms: 10x3 + -10x3 = 0 -6x + 25x2 + 0 = 72 + 24x2 + 10x3 + -10x3 -6x + 25x2 = 72 + 24x2 + 10x3 + -10x3 Combine like terms: 10x3 + -10x3 = 0 -6x + 25x2 = 72 + 24x2 + 0 -6x + 25x2 = 72 + 24x2 Solving -6x + 25x2 = 72 + 24x2 Solving for variable 'x'. Reorder the terms: -72 + -6x + 25x2 + -24x2 = 72 + 24x2 + -72 + -24x2 Combine like terms: 25x2 + -24x2 = 1x2 -72 + -6x + 1x2 = 72 + 24x2 + -72 + -24x2 Reorder the terms: -72 + -6x + 1x2 = 72 + -72 + 24x2 + -24x2 Combine like terms: 72 + -72 = 0 -72 + -6x + 1x2 = 0 + 24x2 + -24x2 -72 + -6x + 1x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -72 + -6x + 1x2 = 0 Factor a trinomial. (-6 + -1x)(12 + -1x) = 0Subproblem 1
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 2
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 = 12Solution
x = {-6, 12}
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