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Simplifying (4x3 + -5x2 + 6x) + (3x3 + 7x2 + -11x) = 0 Reorder the terms: (6x + -5x2 + 4x3) + (3x3 + 7x2 + -11x) = 0 Remove parenthesis around (6x + -5x2 + 4x3) 6x + -5x2 + 4x3 + (3x3 + 7x2 + -11x) = 0 Reorder the terms: 6x + -5x2 + 4x3 + (-11x + 7x2 + 3x3) = 0 Remove parenthesis around (-11x + 7x2 + 3x3) 6x + -5x2 + 4x3 + -11x + 7x2 + 3x3 = 0 Reorder the terms: 6x + -11x + -5x2 + 7x2 + 4x3 + 3x3 = 0 Combine like terms: 6x + -11x = -5x -5x + -5x2 + 7x2 + 4x3 + 3x3 = 0 Combine like terms: -5x2 + 7x2 = 2x2 -5x + 2x2 + 4x3 + 3x3 = 0 Combine like terms: 4x3 + 3x3 = 7x3 -5x + 2x2 + 7x3 = 0 Solving -5x + 2x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 2x + 7x2) = 0 Factor a trinomial. x((-1 + -1x)(5 + -7x)) = 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 '(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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