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Simplifying 15x + 60 + -1(x + 3)(x + 4) = 12x + 36 Reorder the terms: 15x + 60 + -1(3 + x)(x + 4) = 12x + 36 Reorder the terms: 15x + 60 + -1(3 + x)(4 + x) = 12x + 36 Multiply (3 + x) * (4 + x) 15x + 60 + -1(3(4 + x) + x(4 + x)) = 12x + 36 15x + 60 + -1((4 * 3 + x * 3) + x(4 + x)) = 12x + 36 15x + 60 + -1((12 + 3x) + x(4 + x)) = 12x + 36 15x + 60 + -1(12 + 3x + (4 * x + x * x)) = 12x + 36 15x + 60 + -1(12 + 3x + (4x + x2)) = 12x + 36 Combine like terms: 3x + 4x = 7x 15x + 60 + -1(12 + 7x + x2) = 12x + 36 15x + 60 + (12 * -1 + 7x * -1 + x2 * -1) = 12x + 36 15x + 60 + (-12 + -7x + -1x2) = 12x + 36 Reorder the terms: 60 + -12 + 15x + -7x + -1x2 = 12x + 36 Combine like terms: 60 + -12 = 48 48 + 15x + -7x + -1x2 = 12x + 36 Combine like terms: 15x + -7x = 8x 48 + 8x + -1x2 = 12x + 36 Reorder the terms: 48 + 8x + -1x2 = 36 + 12x Solving 48 + 8x + -1x2 = 36 + 12x Solving for variable 'x'. Reorder the terms: 48 + -36 + 8x + -12x + -1x2 = 36 + 12x + -36 + -12x Combine like terms: 48 + -36 = 12 12 + 8x + -12x + -1x2 = 36 + 12x + -36 + -12x Combine like terms: 8x + -12x = -4x 12 + -4x + -1x2 = 36 + 12x + -36 + -12x Reorder the terms: 12 + -4x + -1x2 = 36 + -36 + 12x + -12x Combine like terms: 36 + -36 = 0 12 + -4x + -1x2 = 0 + 12x + -12x 12 + -4x + -1x2 = 12x + -12x Combine like terms: 12x + -12x = 0 12 + -4x + -1x2 = 0 Factor a trinomial. (2 + -1x)(6 + x) = 0Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = {2, -6}
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