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Simplifying (2x + 5)(1 + -3x) + (2x + 5)(2x + -3) = 0 Reorder the terms: (5 + 2x)(1 + -3x) + (2x + 5)(2x + -3) = 0 Multiply (5 + 2x) * (1 + -3x) (5(1 + -3x) + 2x * (1 + -3x)) + (2x + 5)(2x + -3) = 0 ((1 * 5 + -3x * 5) + 2x * (1 + -3x)) + (2x + 5)(2x + -3) = 0 ((5 + -15x) + 2x * (1 + -3x)) + (2x + 5)(2x + -3) = 0 (5 + -15x + (1 * 2x + -3x * 2x)) + (2x + 5)(2x + -3) = 0 (5 + -15x + (2x + -6x2)) + (2x + 5)(2x + -3) = 0 Combine like terms: -15x + 2x = -13x (5 + -13x + -6x2) + (2x + 5)(2x + -3) = 0 Reorder the terms: 5 + -13x + -6x2 + (5 + 2x)(2x + -3) = 0 Reorder the terms: 5 + -13x + -6x2 + (5 + 2x)(-3 + 2x) = 0 Multiply (5 + 2x) * (-3 + 2x) 5 + -13x + -6x2 + (5(-3 + 2x) + 2x * (-3 + 2x)) = 0 5 + -13x + -6x2 + ((-3 * 5 + 2x * 5) + 2x * (-3 + 2x)) = 0 5 + -13x + -6x2 + ((-15 + 10x) + 2x * (-3 + 2x)) = 0 5 + -13x + -6x2 + (-15 + 10x + (-3 * 2x + 2x * 2x)) = 0 5 + -13x + -6x2 + (-15 + 10x + (-6x + 4x2)) = 0 Combine like terms: 10x + -6x = 4x 5 + -13x + -6x2 + (-15 + 4x + 4x2) = 0 Reorder the terms: 5 + -15 + -13x + 4x + -6x2 + 4x2 = 0 Combine like terms: 5 + -15 = -10 -10 + -13x + 4x + -6x2 + 4x2 = 0 Combine like terms: -13x + 4x = -9x -10 + -9x + -6x2 + 4x2 = 0 Combine like terms: -6x2 + 4x2 = -2x2 -10 + -9x + -2x2 = 0 Solving -10 + -9x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 9x + 2x2) = 0 Factor a trinomial. -1((5 + 2x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 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 = {-2.5, -2}
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