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Simplifying 0 = 36x3 + -57x2 + 12x Reorder the terms: 0 = 12x + -57x2 + 36x3 Solving 0 = 12x + -57x2 + 36x3 Solving for variable 'x'. Remove the zero: -12x + 57x2 + -36x3 = 12x + -57x2 + 36x3 + -12x + 57x2 + -36x3 Reorder the terms: -12x + 57x2 + -36x3 = 12x + -12x + -57x2 + 57x2 + 36x3 + -36x3 Combine like terms: 12x + -12x = 0 -12x + 57x2 + -36x3 = 0 + -57x2 + 57x2 + 36x3 + -36x3 -12x + 57x2 + -36x3 = -57x2 + 57x2 + 36x3 + -36x3 Combine like terms: -57x2 + 57x2 = 0 -12x + 57x2 + -36x3 = 0 + 36x3 + -36x3 -12x + 57x2 + -36x3 = 36x3 + -36x3 Combine like terms: 36x3 + -36x3 = 0 -12x + 57x2 + -36x3 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-4 + 19x + -12x2) = 0 Factor a trinomial. 3x((-4 + 3x)(1 + -4x)) = 0 Ignore the factor 3.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 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {0, 1.333333333, 0.25}
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