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Simplifying (2x + -3)(3x + -5) = (2x + -3)(5x + -1) Reorder the terms: (-3 + 2x)(3x + -5) = (2x + -3)(5x + -1) Reorder the terms: (-3 + 2x)(-5 + 3x) = (2x + -3)(5x + -1) Multiply (-3 + 2x) * (-5 + 3x) (-3(-5 + 3x) + 2x * (-5 + 3x)) = (2x + -3)(5x + -1) ((-5 * -3 + 3x * -3) + 2x * (-5 + 3x)) = (2x + -3)(5x + -1) ((15 + -9x) + 2x * (-5 + 3x)) = (2x + -3)(5x + -1) (15 + -9x + (-5 * 2x + 3x * 2x)) = (2x + -3)(5x + -1) (15 + -9x + (-10x + 6x2)) = (2x + -3)(5x + -1) Combine like terms: -9x + -10x = -19x (15 + -19x + 6x2) = (2x + -3)(5x + -1) Reorder the terms: 15 + -19x + 6x2 = (-3 + 2x)(5x + -1) Reorder the terms: 15 + -19x + 6x2 = (-3 + 2x)(-1 + 5x) Multiply (-3 + 2x) * (-1 + 5x) 15 + -19x + 6x2 = (-3(-1 + 5x) + 2x * (-1 + 5x)) 15 + -19x + 6x2 = ((-1 * -3 + 5x * -3) + 2x * (-1 + 5x)) 15 + -19x + 6x2 = ((3 + -15x) + 2x * (-1 + 5x)) 15 + -19x + 6x2 = (3 + -15x + (-1 * 2x + 5x * 2x)) 15 + -19x + 6x2 = (3 + -15x + (-2x + 10x2)) Combine like terms: -15x + -2x = -17x 15 + -19x + 6x2 = (3 + -17x + 10x2) Solving 15 + -19x + 6x2 = 3 + -17x + 10x2 Solving for variable 'x'. Reorder the terms: 15 + -3 + -19x + 17x + 6x2 + -10x2 = 3 + -17x + 10x2 + -3 + 17x + -10x2 Combine like terms: 15 + -3 = 12 12 + -19x + 17x + 6x2 + -10x2 = 3 + -17x + 10x2 + -3 + 17x + -10x2 Combine like terms: -19x + 17x = -2x 12 + -2x + 6x2 + -10x2 = 3 + -17x + 10x2 + -3 + 17x + -10x2 Combine like terms: 6x2 + -10x2 = -4x2 12 + -2x + -4x2 = 3 + -17x + 10x2 + -3 + 17x + -10x2 Reorder the terms: 12 + -2x + -4x2 = 3 + -3 + -17x + 17x + 10x2 + -10x2 Combine like terms: 3 + -3 = 0 12 + -2x + -4x2 = 0 + -17x + 17x + 10x2 + -10x2 12 + -2x + -4x2 = -17x + 17x + 10x2 + -10x2 Combine like terms: -17x + 17x = 0 12 + -2x + -4x2 = 0 + 10x2 + -10x2 12 + -2x + -4x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 12 + -2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -1x + -2x2) = 0 Factor a trinomial. 2((3 + -2x)(2 + x)) = 0 Ignore the factor 2.Subproblem 1
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 = 1.5Subproblem 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 = {1.5, -2}
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