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Simplifying x3 = -5x2 + 6x Reorder the terms: x3 = 6x + -5x2 Solving x3 = 6x + -5x2 Solving for variable 'x'. Reorder the terms: -6x + 5x2 + x3 = 6x + -5x2 + -6x + 5x2 Reorder the terms: -6x + 5x2 + x3 = 6x + -6x + -5x2 + 5x2 Combine like terms: 6x + -6x = 0 -6x + 5x2 + x3 = 0 + -5x2 + 5x2 -6x + 5x2 + x3 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -6x + 5x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 5x + x2) = 0 Factor a trinomial. x((-6 + -1x)(1 + -1x)) = 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 '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, -6, 1}
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