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Simplifying 12x = 32 + -5x2 Solving 12x = 32 + -5x2 Solving for variable 'x'. Reorder the terms: -32 + 12x + 5x2 = 32 + -5x2 + -32 + 5x2 Reorder the terms: -32 + 12x + 5x2 = 32 + -32 + -5x2 + 5x2 Combine like terms: 32 + -32 = 0 -32 + 12x + 5x2 = 0 + -5x2 + 5x2 -32 + 12x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -32 + 12x + 5x2 = 0 Factor a trinomial. (-4 + -1x)(8 + -5x) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 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 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6Solution
x = {-4, 1.6}
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