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