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Simplifying 0 = 60x3 + -92x2 + 16x Reorder the terms: 0 = 16x + -92x2 + 60x3 Solving 0 = 16x + -92x2 + 60x3 Solving for variable 'x'. Remove the zero: -16x + 92x2 + -60x3 = 16x + -92x2 + 60x3 + -16x + 92x2 + -60x3 Reorder the terms: -16x + 92x2 + -60x3 = 16x + -16x + -92x2 + 92x2 + 60x3 + -60x3 Combine like terms: 16x + -16x = 0 -16x + 92x2 + -60x3 = 0 + -92x2 + 92x2 + 60x3 + -60x3 -16x + 92x2 + -60x3 = -92x2 + 92x2 + 60x3 + -60x3 Combine like terms: -92x2 + 92x2 = 0 -16x + 92x2 + -60x3 = 0 + 60x3 + -60x3 -16x + 92x2 + -60x3 = 60x3 + -60x3 Combine like terms: 60x3 + -60x3 = 0 -16x + 92x2 + -60x3 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-4 + 23x + -15x2) = 0 Factor a trinomial. 4x((-4 + 3x)(1 + -5x)) = 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 '(-4 + 3x)' equal to zero and attempt to solve: Simplifying -4 + 3x = 0 Solving -4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3x = 0 + 4 3x = 0 + 4 Combine like terms: 0 + 4 = 4 3x = 4 Divide each side by '3'. x = 1.333333333 Simplifying x = 1.333333333Subproblem 3
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Solution
x = {0, 1.333333333, 0.2}
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