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Simplifying (7x3 + -5x2 + 2x) + (7x3 + 9x2 + -12x) = 0 Reorder the terms: (2x + -5x2 + 7x3) + (7x3 + 9x2 + -12x) = 0 Remove parenthesis around (2x + -5x2 + 7x3) 2x + -5x2 + 7x3 + (7x3 + 9x2 + -12x) = 0 Reorder the terms: 2x + -5x2 + 7x3 + (-12x + 9x2 + 7x3) = 0 Remove parenthesis around (-12x + 9x2 + 7x3) 2x + -5x2 + 7x3 + -12x + 9x2 + 7x3 = 0 Reorder the terms: 2x + -12x + -5x2 + 9x2 + 7x3 + 7x3 = 0 Combine like terms: 2x + -12x = -10x -10x + -5x2 + 9x2 + 7x3 + 7x3 = 0 Combine like terms: -5x2 + 9x2 = 4x2 -10x + 4x2 + 7x3 + 7x3 = 0 Combine like terms: 7x3 + 7x3 = 14x3 -10x + 4x2 + 14x3 = 0 Solving -10x + 4x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-5 + 2x + 7x2) = 0 Factor a trinomial. 2x((-1 + -1x)(5 + -7x)) = 0 Ignore the factor 2.Subproblem 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 '(5 + -7x)' equal to zero and attempt to solve: Simplifying 5 + -7x = 0 Solving 5 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7x = 0 + -5 -7x = 0 + -5 Combine like terms: 0 + -5 = -5 -7x = -5 Divide each side by '-7'. x = 0.7142857143 Simplifying x = 0.7142857143Solution
x = {0, -1, 0.7142857143}
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