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Simplifying 0 = 4x3 + -60x2 + 224x Reorder the terms: 0 = 224x + -60x2 + 4x3 Solving 0 = 224x + -60x2 + 4x3 Solving for variable 'x'. Remove the zero: -224x + 60x2 + -4x3 = 224x + -60x2 + 4x3 + -224x + 60x2 + -4x3 Reorder the terms: -224x + 60x2 + -4x3 = 224x + -224x + -60x2 + 60x2 + 4x3 + -4x3 Combine like terms: 224x + -224x = 0 -224x + 60x2 + -4x3 = 0 + -60x2 + 60x2 + 4x3 + -4x3 -224x + 60x2 + -4x3 = -60x2 + 60x2 + 4x3 + -4x3 Combine like terms: -60x2 + 60x2 = 0 -224x + 60x2 + -4x3 = 0 + 4x3 + -4x3 -224x + 60x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -224x + 60x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-56 + 15x + -1x2) = 0 Factor a trinomial. 4x((-8 + x)(7 + -1x)) = 0 Ignore the factor 4.Subproblem 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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 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 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {0, 8, 7}
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