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Simplifying 5x3 = 4x2 + 12x Reorder the terms: 5x3 = 12x + 4x2 Solving 5x3 = 12x + 4x2 Solving for variable 'x'. Reorder the terms: -12x + -4x2 + 5x3 = 12x + 4x2 + -12x + -4x2 Reorder the terms: -12x + -4x2 + 5x3 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 -12x + -4x2 + 5x3 = 0 + 4x2 + -4x2 -12x + -4x2 + 5x3 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -12x + -4x2 + 5x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + -4x + 5x2) = 0 Factor a trinomial. x((-6 + -5x)(2 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 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 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Divide each side by '-5'. x = -1.2 Simplifying x = -1.2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0, -1.2, 2}
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