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Simplifying 8x2 + 14x + -45 = 7x2 + -12x + 75 Reorder the terms: -45 + 14x + 8x2 = 7x2 + -12x + 75 Reorder the terms: -45 + 14x + 8x2 = 75 + -12x + 7x2 Solving -45 + 14x + 8x2 = 75 + -12x + 7x2 Solving for variable 'x'. Reorder the terms: -45 + -75 + 14x + 12x + 8x2 + -7x2 = 75 + -12x + 7x2 + -75 + 12x + -7x2 Combine like terms: -45 + -75 = -120 -120 + 14x + 12x + 8x2 + -7x2 = 75 + -12x + 7x2 + -75 + 12x + -7x2 Combine like terms: 14x + 12x = 26x -120 + 26x + 8x2 + -7x2 = 75 + -12x + 7x2 + -75 + 12x + -7x2 Combine like terms: 8x2 + -7x2 = 1x2 -120 + 26x + 1x2 = 75 + -12x + 7x2 + -75 + 12x + -7x2 Reorder the terms: -120 + 26x + 1x2 = 75 + -75 + -12x + 12x + 7x2 + -7x2 Combine like terms: 75 + -75 = 0 -120 + 26x + 1x2 = 0 + -12x + 12x + 7x2 + -7x2 -120 + 26x + 1x2 = -12x + 12x + 7x2 + -7x2 Combine like terms: -12x + 12x = 0 -120 + 26x + 1x2 = 0 + 7x2 + -7x2 -120 + 26x + 1x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -120 + 26x + 1x2 = 0 Factor a trinomial. (-30 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-30 + -1x)' equal to zero and attempt to solve: Simplifying -30 + -1x = 0 Solving -30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + -1x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -1x = 0 + 30 -1x = 0 + 30 Combine like terms: 0 + 30 = 30 -1x = 30 Divide each side by '-1'. x = -30 Simplifying x = -30Subproblem 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 = {-30, 4}
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