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Simplifying x(8x + 21) = 3x2 + -16x + 72 Reorder the terms: x(21 + 8x) = 3x2 + -16x + 72 (21 * x + 8x * x) = 3x2 + -16x + 72 (21x + 8x2) = 3x2 + -16x + 72 Reorder the terms: 21x + 8x2 = 72 + -16x + 3x2 Solving 21x + 8x2 = 72 + -16x + 3x2 Solving for variable 'x'. Reorder the terms: -72 + 21x + 16x + 8x2 + -3x2 = 72 + -16x + 3x2 + -72 + 16x + -3x2 Combine like terms: 21x + 16x = 37x -72 + 37x + 8x2 + -3x2 = 72 + -16x + 3x2 + -72 + 16x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -72 + 37x + 5x2 = 72 + -16x + 3x2 + -72 + 16x + -3x2 Reorder the terms: -72 + 37x + 5x2 = 72 + -72 + -16x + 16x + 3x2 + -3x2 Combine like terms: 72 + -72 = 0 -72 + 37x + 5x2 = 0 + -16x + 16x + 3x2 + -3x2 -72 + 37x + 5x2 = -16x + 16x + 3x2 + -3x2 Combine like terms: -16x + 16x = 0 -72 + 37x + 5x2 = 0 + 3x2 + -3x2 -72 + 37x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -72 + 37x + 5x2 = 0 Factor a trinomial. (-9 + -1x)(8 + -5x) = 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 '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6Solution
x = {-9, 1.6}
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