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Simplifying 2x2 + 23x + 60 = x2 + 6x Reorder the terms: 60 + 23x + 2x2 = x2 + 6x Reorder the terms: 60 + 23x + 2x2 = 6x + x2 Solving 60 + 23x + 2x2 = 6x + x2 Solving for variable 'x'. Reorder the terms: 60 + 23x + -6x + 2x2 + -1x2 = 6x + x2 + -6x + -1x2 Combine like terms: 23x + -6x = 17x 60 + 17x + 2x2 + -1x2 = 6x + x2 + -6x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 60 + 17x + 1x2 = 6x + x2 + -6x + -1x2 Reorder the terms: 60 + 17x + 1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 60 + 17x + 1x2 = 0 + x2 + -1x2 60 + 17x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 60 + 17x + 1x2 = 0 Factor a trinomial. (12 + x)(5 + x) = 0Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {-12, -5}
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