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Simplifying 0 = -1x3 + 11x2 + 12x Reorder the terms: 0 = 12x + 11x2 + -1x3 Solving 0 = 12x + 11x2 + -1x3 Solving for variable 'x'. Remove the zero: -12x + -11x2 + x3 = 12x + 11x2 + -1x3 + -12x + -11x2 + x3 Reorder the terms: -12x + -11x2 + x3 = 12x + -12x + 11x2 + -11x2 + -1x3 + x3 Combine like terms: 12x + -12x = 0 -12x + -11x2 + x3 = 0 + 11x2 + -11x2 + -1x3 + x3 -12x + -11x2 + x3 = 11x2 + -11x2 + -1x3 + x3 Combine like terms: 11x2 + -11x2 = 0 -12x + -11x2 + x3 = 0 + -1x3 + x3 -12x + -11x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -12x + -11x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + -11x + x2) = 0 Factor a trinomial. x((-1 + -1x)(12 + -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 '(-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 = -1Subproblem 3
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {0, -1, 12}
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