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Simplifying 12x3(x + 5) = 24x2 + 11x3(x + 5) Reorder the terms: 12x3(5 + x) = 24x2 + 11x3(x + 5) (5 * 12x3 + x * 12x3) = 24x2 + 11x3(x + 5) (60x3 + 12x4) = 24x2 + 11x3(x + 5) Reorder the terms: 60x3 + 12x4 = 24x2 + 11x3(5 + x) 60x3 + 12x4 = 24x2 + (5 * 11x3 + x * 11x3) 60x3 + 12x4 = 24x2 + (55x3 + 11x4) Solving 60x3 + 12x4 = 24x2 + 55x3 + 11x4 Solving for variable 'x'. Reorder the terms: -24x2 + 60x3 + -55x3 + 12x4 + -11x4 = 24x2 + 55x3 + 11x4 + -24x2 + -55x3 + -11x4 Combine like terms: 60x3 + -55x3 = 5x3 -24x2 + 5x3 + 12x4 + -11x4 = 24x2 + 55x3 + 11x4 + -24x2 + -55x3 + -11x4 Combine like terms: 12x4 + -11x4 = 1x4 -24x2 + 5x3 + 1x4 = 24x2 + 55x3 + 11x4 + -24x2 + -55x3 + -11x4 Reorder the terms: -24x2 + 5x3 + 1x4 = 24x2 + -24x2 + 55x3 + -55x3 + 11x4 + -11x4 Combine like terms: 24x2 + -24x2 = 0 -24x2 + 5x3 + 1x4 = 0 + 55x3 + -55x3 + 11x4 + -11x4 -24x2 + 5x3 + 1x4 = 55x3 + -55x3 + 11x4 + -11x4 Combine like terms: 55x3 + -55x3 = 0 -24x2 + 5x3 + 1x4 = 0 + 11x4 + -11x4 -24x2 + 5x3 + 1x4 = 11x4 + -11x4 Combine like terms: 11x4 + -11x4 = 0 -24x2 + 5x3 + 1x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-24 + 5x + x2) = 0 Factor a trinomial. x2((-8 + -1x)(3 + -1x)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
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 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, -8, 3}
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