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Simplifying x(5x + 12) = 2x2 + -8x + 63 Reorder the terms: x(12 + 5x) = 2x2 + -8x + 63 (12 * x + 5x * x) = 2x2 + -8x + 63 (12x + 5x2) = 2x2 + -8x + 63 Reorder the terms: 12x + 5x2 = 63 + -8x + 2x2 Solving 12x + 5x2 = 63 + -8x + 2x2 Solving for variable 'x'. Reorder the terms: -63 + 12x + 8x + 5x2 + -2x2 = 63 + -8x + 2x2 + -63 + 8x + -2x2 Combine like terms: 12x + 8x = 20x -63 + 20x + 5x2 + -2x2 = 63 + -8x + 2x2 + -63 + 8x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -63 + 20x + 3x2 = 63 + -8x + 2x2 + -63 + 8x + -2x2 Reorder the terms: -63 + 20x + 3x2 = 63 + -63 + -8x + 8x + 2x2 + -2x2 Combine like terms: 63 + -63 = 0 -63 + 20x + 3x2 = 0 + -8x + 8x + 2x2 + -2x2 -63 + 20x + 3x2 = -8x + 8x + 2x2 + -2x2 Combine like terms: -8x + 8x = 0 -63 + 20x + 3x2 = 0 + 2x2 + -2x2 -63 + 20x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -63 + 20x + 3x2 = 0 Factor a trinomial. (-9 + -1x)(7 + -3x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve: Simplifying 7 + -3x = 0 Solving 7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3x = 0 + -7 -3x = 0 + -7 Combine like terms: 0 + -7 = -7 -3x = -7 Divide each side by '-3'. x = 2.333333333 Simplifying x = 2.333333333Solution
x = {-9, 2.333333333}
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