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Simplifying 0 = -4x3 + 4x2 + 15x Reorder the terms: 0 = 15x + 4x2 + -4x3 Solving 0 = 15x + 4x2 + -4x3 Solving for variable 'x'. Remove the zero: -15x + -4x2 + 4x3 = 15x + 4x2 + -4x3 + -15x + -4x2 + 4x3 Reorder the terms: -15x + -4x2 + 4x3 = 15x + -15x + 4x2 + -4x2 + -4x3 + 4x3 Combine like terms: 15x + -15x = 0 -15x + -4x2 + 4x3 = 0 + 4x2 + -4x2 + -4x3 + 4x3 -15x + -4x2 + 4x3 = 4x2 + -4x2 + -4x3 + 4x3 Combine like terms: 4x2 + -4x2 = 0 -15x + -4x2 + 4x3 = 0 + -4x3 + 4x3 -15x + -4x2 + 4x3 = -4x3 + 4x3 Combine like terms: -4x3 + 4x3 = 0 -15x + -4x2 + 4x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-15 + -4x + 4x2) = 0 Factor a trinomial. x((-3 + -2x)(5 + -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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {0, -1.5, 2.5}
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