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Simplifying (9x3 + -6x2 + 5x) + (6x3 + 8x2 + -13x) = 0 Reorder the terms: (5x + -6x2 + 9x3) + (6x3 + 8x2 + -13x) = 0 Remove parenthesis around (5x + -6x2 + 9x3) 5x + -6x2 + 9x3 + (6x3 + 8x2 + -13x) = 0 Reorder the terms: 5x + -6x2 + 9x3 + (-13x + 8x2 + 6x3) = 0 Remove parenthesis around (-13x + 8x2 + 6x3) 5x + -6x2 + 9x3 + -13x + 8x2 + 6x3 = 0 Reorder the terms: 5x + -13x + -6x2 + 8x2 + 9x3 + 6x3 = 0 Combine like terms: 5x + -13x = -8x -8x + -6x2 + 8x2 + 9x3 + 6x3 = 0 Combine like terms: -6x2 + 8x2 = 2x2 -8x + 2x2 + 9x3 + 6x3 = 0 Combine like terms: 9x3 + 6x3 = 15x3 -8x + 2x2 + 15x3 = 0 Solving -8x + 2x2 + 15x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + 2x + 15x2) = 0 Factor a trinomial. x((-4 + -5x)(2 + -3x)) = 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 '(-4 + -5x)' equal to zero and attempt to solve: Simplifying -4 + -5x = 0 Solving -4 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x = 0 + 4 -5x = 0 + 4 Combine like terms: 0 + 4 = 4 -5x = 4 Divide each side by '-5'. x = -0.8 Simplifying x = -0.8Subproblem 3
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {0, -0.8, 0.6666666667}
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