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Simplifying (-6x3 + 6x2 + -6x + 5) + (7x3 + 2x2 + -3x + -5) = 0 Reorder the terms: (5 + -6x + 6x2 + -6x3) + (7x3 + 2x2 + -3x + -5) = 0 Remove parenthesis around (5 + -6x + 6x2 + -6x3) 5 + -6x + 6x2 + -6x3 + (7x3 + 2x2 + -3x + -5) = 0 Reorder the terms: 5 + -6x + 6x2 + -6x3 + (-5 + -3x + 2x2 + 7x3) = 0 Remove parenthesis around (-5 + -3x + 2x2 + 7x3) 5 + -6x + 6x2 + -6x3 + -5 + -3x + 2x2 + 7x3 = 0 Reorder the terms: 5 + -5 + -6x + -3x + 6x2 + 2x2 + -6x3 + 7x3 = 0 Combine like terms: 5 + -5 = 0 0 + -6x + -3x + 6x2 + 2x2 + -6x3 + 7x3 = 0 -6x + -3x + 6x2 + 2x2 + -6x3 + 7x3 = 0 Combine like terms: -6x + -3x = -9x -9x + 6x2 + 2x2 + -6x3 + 7x3 = 0 Combine like terms: 6x2 + 2x2 = 8x2 -9x + 8x2 + -6x3 + 7x3 = 0 Combine like terms: -6x3 + 7x3 = 1x3 -9x + 8x2 + 1x3 = 0 Solving -9x + 8x2 + 1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-9 + 8x + x2) = 0 Factor a trinomial. x((-9 + -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 '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 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, -9, 1}
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