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Simplifying 2x2 + -7 + 4x2 + -6x + 40 + 18x + 3 = 180 Reorder the terms: -7 + 40 + 3 + -6x + 18x + 2x2 + 4x2 = 180 Combine like terms: -7 + 40 = 33 33 + 3 + -6x + 18x + 2x2 + 4x2 = 180 Combine like terms: 33 + 3 = 36 36 + -6x + 18x + 2x2 + 4x2 = 180 Combine like terms: -6x + 18x = 12x 36 + 12x + 2x2 + 4x2 = 180 Combine like terms: 2x2 + 4x2 = 6x2 36 + 12x + 6x2 = 180 Solving 36 + 12x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: 36 + -180 + 12x + 6x2 = 180 + -180 Combine like terms: 36 + -180 = -144 -144 + 12x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -144 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-24 + 2x + x2) = 0 Factor a trinomial. 6((-6 + -1x)(4 + -1x)) = 0 Ignore the factor 6.Subproblem 1
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 = -6Subproblem 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 = {-6, 4}
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