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Simplifying 3x2 + x2 + 12x + 20 = 180 Reorder the terms: 20 + 12x + 3x2 + x2 = 180 Combine like terms: 3x2 + x2 = 4x2 20 + 12x + 4x2 = 180 Solving 20 + 12x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: 20 + -180 + 12x + 4x2 = 180 + -180 Combine like terms: 20 + -180 = -160 -160 + 12x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -160 + 12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + 3x + x2) = 0 Factor a trinomial. 4((-8 + -1x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-8, 5}
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