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Simplifying x(4x + -6) = 54 Reorder the terms: x(-6 + 4x) = 54 (-6 * x + 4x * x) = 54 (-6x + 4x2) = 54 Solving -6x + 4x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + -6x + 4x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -3x + 2x2) = 0 Factor a trinomial. 2((-3 + -1x)(9 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
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 = 4.5Solution
x = {-3, 4.5}
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