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Simplifying 6x2 = 18x + 24 Reorder the terms: 6x2 = 24 + 18x Solving 6x2 = 24 + 18x Solving for variable 'x'. Reorder the terms: -24 + -18x + 6x2 = 24 + 18x + -24 + -18x Reorder the terms: -24 + -18x + 6x2 = 24 + -24 + 18x + -18x Combine like terms: 24 + -24 = 0 -24 + -18x + 6x2 = 0 + 18x + -18x -24 + -18x + 6x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -24 + -18x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + -3x + x2) = 0 Factor a trinomial. 6((-1 + -1x)(4 + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-1, 4}
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