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Simplifying (2x + -3) * x = 54 Reorder the terms: (-3 + 2x) * x = 54 Reorder the terms for easier multiplication: x(-3 + 2x) = 54 (-3 * x + 2x * x) = 54 (-3x + 2x2) = 54 Solving -3x + 2x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + -3x + 2x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -3x + 2x2 = 0 Factor a trinomial. (-9 + -2x)(6 + -1x) = 0Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 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 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 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 = {-4.5, 6}
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