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Simplifying 6x2 + -4x + -10 = 7x2 + -2x + -34 Reorder the terms: -10 + -4x + 6x2 = 7x2 + -2x + -34 Reorder the terms: -10 + -4x + 6x2 = -34 + -2x + 7x2 Solving -10 + -4x + 6x2 = -34 + -2x + 7x2 Solving for variable 'x'. Reorder the terms: -10 + 34 + -4x + 2x + 6x2 + -7x2 = -34 + -2x + 7x2 + 34 + 2x + -7x2 Combine like terms: -10 + 34 = 24 24 + -4x + 2x + 6x2 + -7x2 = -34 + -2x + 7x2 + 34 + 2x + -7x2 Combine like terms: -4x + 2x = -2x 24 + -2x + 6x2 + -7x2 = -34 + -2x + 7x2 + 34 + 2x + -7x2 Combine like terms: 6x2 + -7x2 = -1x2 24 + -2x + -1x2 = -34 + -2x + 7x2 + 34 + 2x + -7x2 Reorder the terms: 24 + -2x + -1x2 = -34 + 34 + -2x + 2x + 7x2 + -7x2 Combine like terms: -34 + 34 = 0 24 + -2x + -1x2 = 0 + -2x + 2x + 7x2 + -7x2 24 + -2x + -1x2 = -2x + 2x + 7x2 + -7x2 Combine like terms: -2x + 2x = 0 24 + -2x + -1x2 = 0 + 7x2 + -7x2 24 + -2x + -1x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 24 + -2x + -1x2 = 0 Factor a trinomial. (4 + -1x)(6 + x) = 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 '(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 = -6Solution
x = {4, -6}
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