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Simplifying (3x + -1)(3x + 5) = (5x + 8)(x + -4) Reorder the terms: (-1 + 3x)(3x + 5) = (5x + 8)(x + -4) Reorder the terms: (-1 + 3x)(5 + 3x) = (5x + 8)(x + -4) Multiply (-1 + 3x) * (5 + 3x) (-1(5 + 3x) + 3x * (5 + 3x)) = (5x + 8)(x + -4) ((5 * -1 + 3x * -1) + 3x * (5 + 3x)) = (5x + 8)(x + -4) ((-5 + -3x) + 3x * (5 + 3x)) = (5x + 8)(x + -4) (-5 + -3x + (5 * 3x + 3x * 3x)) = (5x + 8)(x + -4) (-5 + -3x + (15x + 9x2)) = (5x + 8)(x + -4) Combine like terms: -3x + 15x = 12x (-5 + 12x + 9x2) = (5x + 8)(x + -4) Reorder the terms: -5 + 12x + 9x2 = (8 + 5x)(x + -4) Reorder the terms: -5 + 12x + 9x2 = (8 + 5x)(-4 + x) Multiply (8 + 5x) * (-4 + x) -5 + 12x + 9x2 = (8(-4 + x) + 5x * (-4 + x)) -5 + 12x + 9x2 = ((-4 * 8 + x * 8) + 5x * (-4 + x)) -5 + 12x + 9x2 = ((-32 + 8x) + 5x * (-4 + x)) -5 + 12x + 9x2 = (-32 + 8x + (-4 * 5x + x * 5x)) -5 + 12x + 9x2 = (-32 + 8x + (-20x + 5x2)) Combine like terms: 8x + -20x = -12x -5 + 12x + 9x2 = (-32 + -12x + 5x2) Solving -5 + 12x + 9x2 = -32 + -12x + 5x2 Solving for variable 'x'. Reorder the terms: -5 + 32 + 12x + 12x + 9x2 + -5x2 = -32 + -12x + 5x2 + 32 + 12x + -5x2 Combine like terms: -5 + 32 = 27 27 + 12x + 12x + 9x2 + -5x2 = -32 + -12x + 5x2 + 32 + 12x + -5x2 Combine like terms: 12x + 12x = 24x 27 + 24x + 9x2 + -5x2 = -32 + -12x + 5x2 + 32 + 12x + -5x2 Combine like terms: 9x2 + -5x2 = 4x2 27 + 24x + 4x2 = -32 + -12x + 5x2 + 32 + 12x + -5x2 Reorder the terms: 27 + 24x + 4x2 = -32 + 32 + -12x + 12x + 5x2 + -5x2 Combine like terms: -32 + 32 = 0 27 + 24x + 4x2 = 0 + -12x + 12x + 5x2 + -5x2 27 + 24x + 4x2 = -12x + 12x + 5x2 + -5x2 Combine like terms: -12x + 12x = 0 27 + 24x + 4x2 = 0 + 5x2 + -5x2 27 + 24x + 4x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 27 + 24x + 4x2 = 0 Factor a trinomial. (9 + 2x)(3 + 2x) = 0Subproblem 1
Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {-4.5, -1.5}
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