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Simplifying 0 = -4x4 + 8x3 + 60x2 Reorder the terms: 0 = 60x2 + 8x3 + -4x4 Solving 0 = 60x2 + 8x3 + -4x4 Solving for variable 'x'. Remove the zero: -60x2 + -8x3 + 4x4 = 60x2 + 8x3 + -4x4 + -60x2 + -8x3 + 4x4 Reorder the terms: -60x2 + -8x3 + 4x4 = 60x2 + -60x2 + 8x3 + -8x3 + -4x4 + 4x4 Combine like terms: 60x2 + -60x2 = 0 -60x2 + -8x3 + 4x4 = 0 + 8x3 + -8x3 + -4x4 + 4x4 -60x2 + -8x3 + 4x4 = 8x3 + -8x3 + -4x4 + 4x4 Combine like terms: 8x3 + -8x3 = 0 -60x2 + -8x3 + 4x4 = 0 + -4x4 + 4x4 -60x2 + -8x3 + 4x4 = -4x4 + 4x4 Combine like terms: -4x4 + 4x4 = 0 -60x2 + -8x3 + 4x4 = 0 Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(-15 + -2x + x2) = 0 Factor a trinomial. 4x2((-3 + -1x)(5 + -1x)) = 0 Ignore the factor 4.Subproblem 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 '(-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 = -3Subproblem 3
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 = {0, -3, 5}
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