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Simplifying 0 = 2x3 + 11x2 + -6x Reorder the terms: 0 = -6x + 11x2 + 2x3 Solving 0 = -6x + 11x2 + 2x3 Solving for variable 'x'. Remove the zero: 6x + -11x2 + -2x3 = -6x + 11x2 + 2x3 + 6x + -11x2 + -2x3 Reorder the terms: 6x + -11x2 + -2x3 = -6x + 6x + 11x2 + -11x2 + 2x3 + -2x3 Combine like terms: -6x + 6x = 0 6x + -11x2 + -2x3 = 0 + 11x2 + -11x2 + 2x3 + -2x3 6x + -11x2 + -2x3 = 11x2 + -11x2 + 2x3 + -2x3 Combine like terms: 11x2 + -11x2 = 0 6x + -11x2 + -2x3 = 0 + 2x3 + -2x3 6x + -11x2 + -2x3 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 6x + -11x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(6 + -11x + -2x2) = 0 Factor a trinomial. x((1 + -2x)(6 + x)) = 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 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {0, 0.5, -6}
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