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Simplifying 0 = 12x3 + -23x2 + 5x Reorder the terms: 0 = 5x + -23x2 + 12x3 Solving 0 = 5x + -23x2 + 12x3 Solving for variable 'x'. Remove the zero: -5x + 23x2 + -12x3 = 5x + -23x2 + 12x3 + -5x + 23x2 + -12x3 Reorder the terms: -5x + 23x2 + -12x3 = 5x + -5x + -23x2 + 23x2 + 12x3 + -12x3 Combine like terms: 5x + -5x = 0 -5x + 23x2 + -12x3 = 0 + -23x2 + 23x2 + 12x3 + -12x3 -5x + 23x2 + -12x3 = -23x2 + 23x2 + 12x3 + -12x3 Combine like terms: -23x2 + 23x2 = 0 -5x + 23x2 + -12x3 = 0 + 12x3 + -12x3 -5x + 23x2 + -12x3 = 12x3 + -12x3 Combine like terms: 12x3 + -12x3 = 0 -5x + 23x2 + -12x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 23x + -12x2) = 0 Factor a trinomial. x((-5 + 3x)(1 + -4x)) = 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 '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 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 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Divide each side by '3'. x = 1.666666667 Simplifying x = 1.666666667Subproblem 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, 1.666666667, 0.25}
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