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Simplifying 4x2 + 5x + -7 = 5x2 + -6x + 23 Reorder the terms: -7 + 5x + 4x2 = 5x2 + -6x + 23 Reorder the terms: -7 + 5x + 4x2 = 23 + -6x + 5x2 Solving -7 + 5x + 4x2 = 23 + -6x + 5x2 Solving for variable 'x'. Reorder the terms: -7 + -23 + 5x + 6x + 4x2 + -5x2 = 23 + -6x + 5x2 + -23 + 6x + -5x2 Combine like terms: -7 + -23 = -30 -30 + 5x + 6x + 4x2 + -5x2 = 23 + -6x + 5x2 + -23 + 6x + -5x2 Combine like terms: 5x + 6x = 11x -30 + 11x + 4x2 + -5x2 = 23 + -6x + 5x2 + -23 + 6x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -30 + 11x + -1x2 = 23 + -6x + 5x2 + -23 + 6x + -5x2 Reorder the terms: -30 + 11x + -1x2 = 23 + -23 + -6x + 6x + 5x2 + -5x2 Combine like terms: 23 + -23 = 0 -30 + 11x + -1x2 = 0 + -6x + 6x + 5x2 + -5x2 -30 + 11x + -1x2 = -6x + 6x + 5x2 + -5x2 Combine like terms: -6x + 6x = 0 -30 + 11x + -1x2 = 0 + 5x2 + -5x2 -30 + 11x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -30 + 11x + -1x2 = 0 Factor a trinomial. (-6 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {6, 5}
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