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Simplifying (6x3 + -6x2 + 2x) + (8x3 + 9x2 + -13x) = 0 Reorder the terms: (2x + -6x2 + 6x3) + (8x3 + 9x2 + -13x) = 0 Remove parenthesis around (2x + -6x2 + 6x3) 2x + -6x2 + 6x3 + (8x3 + 9x2 + -13x) = 0 Reorder the terms: 2x + -6x2 + 6x3 + (-13x + 9x2 + 8x3) = 0 Remove parenthesis around (-13x + 9x2 + 8x3) 2x + -6x2 + 6x3 + -13x + 9x2 + 8x3 = 0 Reorder the terms: 2x + -13x + -6x2 + 9x2 + 6x3 + 8x3 = 0 Combine like terms: 2x + -13x = -11x -11x + -6x2 + 9x2 + 6x3 + 8x3 = 0 Combine like terms: -6x2 + 9x2 = 3x2 -11x + 3x2 + 6x3 + 8x3 = 0 Combine like terms: 6x3 + 8x3 = 14x3 -11x + 3x2 + 14x3 = 0 Solving -11x + 3x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-11 + 3x + 14x2) = 0 Factor a trinomial. x((-1 + -1x)(11 + -14x)) = 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 '(11 + -14x)' equal to zero and attempt to solve: Simplifying 11 + -14x = 0 Solving 11 + -14x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -14x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -14x = 0 + -11 -14x = 0 + -11 Combine like terms: 0 + -11 = -11 -14x = -11 Divide each side by '-14'. x = 0.7857142857 Simplifying x = 0.7857142857Solution
x = {0, -1, 0.7857142857}
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