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Simplifying (4x2 + 6x2 + -8x) + -1(x3 + -2x2 + 12x) = 0 Reorder the terms: (-8x + 4x2 + 6x2) + -1(x3 + -2x2 + 12x) = 0 Combine like terms: 4x2 + 6x2 = 10x2 (-8x + 10x2) + -1(x3 + -2x2 + 12x) = 0 Remove parenthesis around (-8x + 10x2) -8x + 10x2 + -1(x3 + -2x2 + 12x) = 0 Reorder the terms: -8x + 10x2 + -1(12x + -2x2 + x3) = 0 -8x + 10x2 + (12x * -1 + -2x2 * -1 + x3 * -1) = 0 -8x + 10x2 + (-12x + 2x2 + -1x3) = 0 Reorder the terms: -8x + -12x + 10x2 + 2x2 + -1x3 = 0 Combine like terms: -8x + -12x = -20x -20x + 10x2 + 2x2 + -1x3 = 0 Combine like terms: 10x2 + 2x2 = 12x2 -20x + 12x2 + -1x3 = 0 Solving -20x + 12x2 + -1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-20 + 12x + -1x2) = 0 Factor a trinomial. x((-10 + x)(2 + -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 '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Simplifying x = 10Subproblem 3
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 = 2Solution
x = {0, 10, 2}
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