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Simplifying (4x3 + 6x2 + -12x) + -1(3x3 + 5x2 + 18x) = 0 Reorder the terms: (-12x + 6x2 + 4x3) + -1(3x3 + 5x2 + 18x) = 0 Remove parenthesis around (-12x + 6x2 + 4x3) -12x + 6x2 + 4x3 + -1(3x3 + 5x2 + 18x) = 0 Reorder the terms: -12x + 6x2 + 4x3 + -1(18x + 5x2 + 3x3) = 0 -12x + 6x2 + 4x3 + (18x * -1 + 5x2 * -1 + 3x3 * -1) = 0 -12x + 6x2 + 4x3 + (-18x + -5x2 + -3x3) = 0 Reorder the terms: -12x + -18x + 6x2 + -5x2 + 4x3 + -3x3 = 0 Combine like terms: -12x + -18x = -30x -30x + 6x2 + -5x2 + 4x3 + -3x3 = 0 Combine like terms: 6x2 + -5x2 = 1x2 -30x + 1x2 + 4x3 + -3x3 = 0 Combine like terms: 4x3 + -3x3 = 1x3 -30x + 1x2 + 1x3 = 0 Solving -30x + 1x2 + 1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-30 + x + x2) = 0 Factor a trinomial. x((-6 + -1x)(5 + -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 '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, -6, 5}
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