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Simplifying (3x + 2)(x + -3) + (3x + 2)(5x + 1) = 0 Reorder the terms: (2 + 3x)(x + -3) + (3x + 2)(5x + 1) = 0 Reorder the terms: (2 + 3x)(-3 + x) + (3x + 2)(5x + 1) = 0 Multiply (2 + 3x) * (-3 + x) (2(-3 + x) + 3x * (-3 + x)) + (3x + 2)(5x + 1) = 0 ((-3 * 2 + x * 2) + 3x * (-3 + x)) + (3x + 2)(5x + 1) = 0 ((-6 + 2x) + 3x * (-3 + x)) + (3x + 2)(5x + 1) = 0 (-6 + 2x + (-3 * 3x + x * 3x)) + (3x + 2)(5x + 1) = 0 (-6 + 2x + (-9x + 3x2)) + (3x + 2)(5x + 1) = 0 Combine like terms: 2x + -9x = -7x (-6 + -7x + 3x2) + (3x + 2)(5x + 1) = 0 Reorder the terms: -6 + -7x + 3x2 + (2 + 3x)(5x + 1) = 0 Reorder the terms: -6 + -7x + 3x2 + (2 + 3x)(1 + 5x) = 0 Multiply (2 + 3x) * (1 + 5x) -6 + -7x + 3x2 + (2(1 + 5x) + 3x * (1 + 5x)) = 0 -6 + -7x + 3x2 + ((1 * 2 + 5x * 2) + 3x * (1 + 5x)) = 0 -6 + -7x + 3x2 + ((2 + 10x) + 3x * (1 + 5x)) = 0 -6 + -7x + 3x2 + (2 + 10x + (1 * 3x + 5x * 3x)) = 0 -6 + -7x + 3x2 + (2 + 10x + (3x + 15x2)) = 0 Combine like terms: 10x + 3x = 13x -6 + -7x + 3x2 + (2 + 13x + 15x2) = 0 Reorder the terms: -6 + 2 + -7x + 13x + 3x2 + 15x2 = 0 Combine like terms: -6 + 2 = -4 -4 + -7x + 13x + 3x2 + 15x2 = 0 Combine like terms: -7x + 13x = 6x -4 + 6x + 3x2 + 15x2 = 0 Combine like terms: 3x2 + 15x2 = 18x2 -4 + 6x + 18x2 = 0 Solving -4 + 6x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 3x + 9x2) = 0 Factor a trinomial. 2((-2 + -3x)(1 + -3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve: Simplifying -2 + -3x = 0 Solving -2 + -3x = 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 + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x = 0 + 2 -3x = 0 + 2 Combine like terms: 0 + 2 = 2 -3x = 2 Divide each side by '-3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-0.6666666667, 0.3333333333}
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