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Simplifying (4x)(x) + (x + 3)(2x) = 180 Remove parenthesis around (4x) 4x(x) + (x + 3)(2x) = 180 Multiply x * x 4x2 + (x + 3)(2x) = 180 Reorder the terms: 4x2 + (3 + x)(2x) = 180 Remove parenthesis around (2x) 4x2 + (3 + x) * 2x = 180 Reorder the terms for easier multiplication: 4x2 + 2x(3 + x) = 180 4x2 + (3 * 2x + x * 2x) = 180 4x2 + (6x + 2x2) = 180 Reorder the terms: 6x + 4x2 + 2x2 = 180 Combine like terms: 4x2 + 2x2 = 6x2 6x + 6x2 = 180 Solving 6x + 6x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 6x + 6x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-30 + x + x2) = 0 Factor a trinomial. 6((-6 + -1x)(5 + -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 '(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 = {-6, 5}
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