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Simplifying (2x + 1)(x + 4) + -1(x + 4)(3x + -5) = 0 Reorder the terms: (1 + 2x)(x + 4) + -1(x + 4)(3x + -5) = 0 Reorder the terms: (1 + 2x)(4 + x) + -1(x + 4)(3x + -5) = 0 Multiply (1 + 2x) * (4 + x) (1(4 + x) + 2x * (4 + x)) + -1(x + 4)(3x + -5) = 0 ((4 * 1 + x * 1) + 2x * (4 + x)) + -1(x + 4)(3x + -5) = 0 ((4 + 1x) + 2x * (4 + x)) + -1(x + 4)(3x + -5) = 0 (4 + 1x + (4 * 2x + x * 2x)) + -1(x + 4)(3x + -5) = 0 (4 + 1x + (8x + 2x2)) + -1(x + 4)(3x + -5) = 0 Combine like terms: 1x + 8x = 9x (4 + 9x + 2x2) + -1(x + 4)(3x + -5) = 0 Reorder the terms: 4 + 9x + 2x2 + -1(4 + x)(3x + -5) = 0 Reorder the terms: 4 + 9x + 2x2 + -1(4 + x)(-5 + 3x) = 0 Multiply (4 + x) * (-5 + 3x) 4 + 9x + 2x2 + -1(4(-5 + 3x) + x(-5 + 3x)) = 0 4 + 9x + 2x2 + -1((-5 * 4 + 3x * 4) + x(-5 + 3x)) = 0 4 + 9x + 2x2 + -1((-20 + 12x) + x(-5 + 3x)) = 0 4 + 9x + 2x2 + -1(-20 + 12x + (-5 * x + 3x * x)) = 0 4 + 9x + 2x2 + -1(-20 + 12x + (-5x + 3x2)) = 0 Combine like terms: 12x + -5x = 7x 4 + 9x + 2x2 + -1(-20 + 7x + 3x2) = 0 4 + 9x + 2x2 + (-20 * -1 + 7x * -1 + 3x2 * -1) = 0 4 + 9x + 2x2 + (20 + -7x + -3x2) = 0 Reorder the terms: 4 + 20 + 9x + -7x + 2x2 + -3x2 = 0 Combine like terms: 4 + 20 = 24 24 + 9x + -7x + 2x2 + -3x2 = 0 Combine like terms: 9x + -7x = 2x 24 + 2x + 2x2 + -3x2 = 0 Combine like terms: 2x2 + -3x2 = -1x2 24 + 2x + -1x2 = 0 Solving 24 + 2x + -1x2 = 0 Solving for variable 'x'. Factor a trinomial. (6 + -1x)(4 + x) = 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {6, -4}
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