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Simplifying 0 = -4x3 + 12x2 + -9x Reorder the terms: 0 = -9x + 12x2 + -4x3 Solving 0 = -9x + 12x2 + -4x3 Solving for variable 'x'. Remove the zero: 9x + -12x2 + 4x3 = -9x + 12x2 + -4x3 + 9x + -12x2 + 4x3 Reorder the terms: 9x + -12x2 + 4x3 = -9x + 9x + 12x2 + -12x2 + -4x3 + 4x3 Combine like terms: -9x + 9x = 0 9x + -12x2 + 4x3 = 0 + 12x2 + -12x2 + -4x3 + 4x3 9x + -12x2 + 4x3 = 12x2 + -12x2 + -4x3 + 4x3 Combine like terms: 12x2 + -12x2 = 0 9x + -12x2 + 4x3 = 0 + -4x3 + 4x3 9x + -12x2 + 4x3 = -4x3 + 4x3 Combine like terms: -4x3 + 4x3 = 0 9x + -12x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(9 + -12x + 4x2) = 0 Factor a trinomial. x((3 + -2x)(3 + -2x)) = 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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 3
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, 1.5, 1.5}
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