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Simplifying (5x + 12)(5 + -2x) + (5x + 12)(3x + -3) = 0 Reorder the terms: (12 + 5x)(5 + -2x) + (5x + 12)(3x + -3) = 0 Multiply (12 + 5x) * (5 + -2x) (12(5 + -2x) + 5x * (5 + -2x)) + (5x + 12)(3x + -3) = 0 ((5 * 12 + -2x * 12) + 5x * (5 + -2x)) + (5x + 12)(3x + -3) = 0 ((60 + -24x) + 5x * (5 + -2x)) + (5x + 12)(3x + -3) = 0 (60 + -24x + (5 * 5x + -2x * 5x)) + (5x + 12)(3x + -3) = 0 (60 + -24x + (25x + -10x2)) + (5x + 12)(3x + -3) = 0 Combine like terms: -24x + 25x = 1x (60 + 1x + -10x2) + (5x + 12)(3x + -3) = 0 Reorder the terms: 60 + 1x + -10x2 + (12 + 5x)(3x + -3) = 0 Reorder the terms: 60 + 1x + -10x2 + (12 + 5x)(-3 + 3x) = 0 Multiply (12 + 5x) * (-3 + 3x) 60 + 1x + -10x2 + (12(-3 + 3x) + 5x * (-3 + 3x)) = 0 60 + 1x + -10x2 + ((-3 * 12 + 3x * 12) + 5x * (-3 + 3x)) = 0 60 + 1x + -10x2 + ((-36 + 36x) + 5x * (-3 + 3x)) = 0 60 + 1x + -10x2 + (-36 + 36x + (-3 * 5x + 3x * 5x)) = 0 60 + 1x + -10x2 + (-36 + 36x + (-15x + 15x2)) = 0 Combine like terms: 36x + -15x = 21x 60 + 1x + -10x2 + (-36 + 21x + 15x2) = 0 Reorder the terms: 60 + -36 + 1x + 21x + -10x2 + 15x2 = 0 Combine like terms: 60 + -36 = 24 24 + 1x + 21x + -10x2 + 15x2 = 0 Combine like terms: 1x + 21x = 22x 24 + 22x + -10x2 + 15x2 = 0 Combine like terms: -10x2 + 15x2 = 5x2 24 + 22x + 5x2 = 0 Solving 24 + 22x + 5x2 = 0 Solving for variable 'x'. Factor a trinomial. (12 + 5x)(2 + x) = 0Subproblem 1
Set the factor '(12 + 5x)' equal to zero and attempt to solve: Simplifying 12 + 5x = 0 Solving 12 + 5x = 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 + 5x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 5x = 0 + -12 5x = 0 + -12 Combine like terms: 0 + -12 = -12 5x = -12 Divide each side by '5'. x = -2.4 Simplifying x = -2.4Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-2.4, -2}
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