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Simplifying 6x2 + 4x + -15 = 27 + -25x Reorder the terms: -15 + 4x + 6x2 = 27 + -25x Solving -15 + 4x + 6x2 = 27 + -25x Solving for variable 'x'. Reorder the terms: -15 + -27 + 4x + 25x + 6x2 = 27 + -25x + -27 + 25x Combine like terms: -15 + -27 = -42 -42 + 4x + 25x + 6x2 = 27 + -25x + -27 + 25x Combine like terms: 4x + 25x = 29x -42 + 29x + 6x2 = 27 + -25x + -27 + 25x Reorder the terms: -42 + 29x + 6x2 = 27 + -27 + -25x + 25x Combine like terms: 27 + -27 = 0 -42 + 29x + 6x2 = 0 + -25x + 25x -42 + 29x + 6x2 = -25x + 25x Combine like terms: -25x + 25x = 0 -42 + 29x + 6x2 = 0 Factor a trinomial. (-6 + -1x)(7 + -6x) = 0Subproblem 1
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 = -6Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve: Simplifying 7 + -6x = 0 Solving 7 + -6x = 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 + -6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x = 0 + -7 -6x = 0 + -7 Combine like terms: 0 + -7 = -7 -6x = -7 Divide each side by '-6'. x = 1.166666667 Simplifying x = 1.166666667Solution
x = {-6, 1.166666667}
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