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Simplifying 4x + -12 + -20 = x2 + -8x Reorder the terms: -12 + -20 + 4x = x2 + -8x Combine like terms: -12 + -20 = -32 -32 + 4x = x2 + -8x Reorder the terms: -32 + 4x = -8x + x2 Solving -32 + 4x = -8x + x2 Solving for variable 'x'. Combine like terms: 4x + 8x = 12x -32 + 12x + -1x2 = -8x + x2 + 8x + -1x2 Reorder the terms: -32 + 12x + -1x2 = -8x + 8x + x2 + -1x2 Combine like terms: -8x + 8x = 0 -32 + 12x + -1x2 = 0 + x2 + -1x2 -32 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -32 + 12x + -1x2 = 0 Factor a trinomial. (-8 + x)(4 + -1x) = 0Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 2
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 = {8, 4}
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