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Simplifying 0 = 4x3 + -36x2 + 81x Reorder the terms: 0 = 81x + -36x2 + 4x3 Solving 0 = 81x + -36x2 + 4x3 Solving for variable 'x'. Remove the zero: -81x + 36x2 + -4x3 = 81x + -36x2 + 4x3 + -81x + 36x2 + -4x3 Reorder the terms: -81x + 36x2 + -4x3 = 81x + -81x + -36x2 + 36x2 + 4x3 + -4x3 Combine like terms: 81x + -81x = 0 -81x + 36x2 + -4x3 = 0 + -36x2 + 36x2 + 4x3 + -4x3 -81x + 36x2 + -4x3 = -36x2 + 36x2 + 4x3 + -4x3 Combine like terms: -36x2 + 36x2 = 0 -81x + 36x2 + -4x3 = 0 + 4x3 + -4x3 -81x + 36x2 + -4x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 -81x + 36x2 + -4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-81 + 36x + -4x2) = 0 Factor a trinomial. x((-9 + 2x)(9 + -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 '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Divide each side by '2'. x = 4.5 Simplifying x = 4.5Subproblem 3
Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {0, 4.5, 4.5}
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