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Simplifying x(5x + 3) = 2x2 + -20x + 36 Reorder the terms: x(3 + 5x) = 2x2 + -20x + 36 (3 * x + 5x * x) = 2x2 + -20x + 36 (3x + 5x2) = 2x2 + -20x + 36 Reorder the terms: 3x + 5x2 = 36 + -20x + 2x2 Solving 3x + 5x2 = 36 + -20x + 2x2 Solving for variable 'x'. Reorder the terms: -36 + 3x + 20x + 5x2 + -2x2 = 36 + -20x + 2x2 + -36 + 20x + -2x2 Combine like terms: 3x + 20x = 23x -36 + 23x + 5x2 + -2x2 = 36 + -20x + 2x2 + -36 + 20x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -36 + 23x + 3x2 = 36 + -20x + 2x2 + -36 + 20x + -2x2 Reorder the terms: -36 + 23x + 3x2 = 36 + -36 + -20x + 20x + 2x2 + -2x2 Combine like terms: 36 + -36 = 0 -36 + 23x + 3x2 = 0 + -20x + 20x + 2x2 + -2x2 -36 + 23x + 3x2 = -20x + 20x + 2x2 + -2x2 Combine like terms: -20x + 20x = 0 -36 + 23x + 3x2 = 0 + 2x2 + -2x2 -36 + 23x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -36 + 23x + 3x2 = 0 Factor a trinomial. (-9 + -1x)(4 + -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 '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {-9, 1.333333333}
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