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Simplifying 8x2 + -5x + -42 = -6x + 7x2 Reorder the terms: -42 + -5x + 8x2 = -6x + 7x2 Solving -42 + -5x + 8x2 = -6x + 7x2 Solving for variable 'x'. Reorder the terms: -42 + -5x + 6x + 8x2 + -7x2 = -6x + 7x2 + 6x + -7x2 Combine like terms: -5x + 6x = 1x -42 + 1x + 8x2 + -7x2 = -6x + 7x2 + 6x + -7x2 Combine like terms: 8x2 + -7x2 = 1x2 -42 + 1x + 1x2 = -6x + 7x2 + 6x + -7x2 Reorder the terms: -42 + 1x + 1x2 = -6x + 6x + 7x2 + -7x2 Combine like terms: -6x + 6x = 0 -42 + 1x + 1x2 = 0 + 7x2 + -7x2 -42 + 1x + 1x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -42 + 1x + 1x2 = 0 Factor a trinomial. (-7 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 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 = 6Solution
x = {-7, 6}
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