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Simplifying 6x2 + -15x = 54 Reorder the terms: -15x + 6x2 = 54 Solving -15x + 6x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + -15x + 6x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -15x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-18 + -5x + 2x2) = 0 Factor a trinomial. 3((-2 + -1x)(9 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 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 = {-2, 4.5}
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