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