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Simplifying (3x + -2)(x + 5) = (2x + 2)(3x + -2) Reorder the terms: (-2 + 3x)(x + 5) = (2x + 2)(3x + -2) Reorder the terms: (-2 + 3x)(5 + x) = (2x + 2)(3x + -2) Multiply (-2 + 3x) * (5 + x) (-2(5 + x) + 3x * (5 + x)) = (2x + 2)(3x + -2) ((5 * -2 + x * -2) + 3x * (5 + x)) = (2x + 2)(3x + -2) ((-10 + -2x) + 3x * (5 + x)) = (2x + 2)(3x + -2) (-10 + -2x + (5 * 3x + x * 3x)) = (2x + 2)(3x + -2) (-10 + -2x + (15x + 3x2)) = (2x + 2)(3x + -2) Combine like terms: -2x + 15x = 13x (-10 + 13x + 3x2) = (2x + 2)(3x + -2) Reorder the terms: -10 + 13x + 3x2 = (2 + 2x)(3x + -2) Reorder the terms: -10 + 13x + 3x2 = (2 + 2x)(-2 + 3x) Multiply (2 + 2x) * (-2 + 3x) -10 + 13x + 3x2 = (2(-2 + 3x) + 2x * (-2 + 3x)) -10 + 13x + 3x2 = ((-2 * 2 + 3x * 2) + 2x * (-2 + 3x)) -10 + 13x + 3x2 = ((-4 + 6x) + 2x * (-2 + 3x)) -10 + 13x + 3x2 = (-4 + 6x + (-2 * 2x + 3x * 2x)) -10 + 13x + 3x2 = (-4 + 6x + (-4x + 6x2)) Combine like terms: 6x + -4x = 2x -10 + 13x + 3x2 = (-4 + 2x + 6x2) Solving -10 + 13x + 3x2 = -4 + 2x + 6x2 Solving for variable 'x'. Reorder the terms: -10 + 4 + 13x + -2x + 3x2 + -6x2 = -4 + 2x + 6x2 + 4 + -2x + -6x2 Combine like terms: -10 + 4 = -6 -6 + 13x + -2x + 3x2 + -6x2 = -4 + 2x + 6x2 + 4 + -2x + -6x2 Combine like terms: 13x + -2x = 11x -6 + 11x + 3x2 + -6x2 = -4 + 2x + 6x2 + 4 + -2x + -6x2 Combine like terms: 3x2 + -6x2 = -3x2 -6 + 11x + -3x2 = -4 + 2x + 6x2 + 4 + -2x + -6x2 Reorder the terms: -6 + 11x + -3x2 = -4 + 4 + 2x + -2x + 6x2 + -6x2 Combine like terms: -4 + 4 = 0 -6 + 11x + -3x2 = 0 + 2x + -2x + 6x2 + -6x2 -6 + 11x + -3x2 = 2x + -2x + 6x2 + -6x2 Combine like terms: 2x + -2x = 0 -6 + 11x + -3x2 = 0 + 6x2 + -6x2 -6 + 11x + -3x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -6 + 11x + -3x2 = 0 Factor a trinomial. (-3 + x)(2 + -3x) = 0Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 2
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 = 0.6666666667Solution
x = {3, 0.6666666667}
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