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Simplifying (3x + 5)(x + -2) + (2x + -3)(x + -2) = 0 Reorder the terms: (5 + 3x)(x + -2) + (2x + -3)(x + -2) = 0 Reorder the terms: (5 + 3x)(-2 + x) + (2x + -3)(x + -2) = 0 Multiply (5 + 3x) * (-2 + x) (5(-2 + x) + 3x * (-2 + x)) + (2x + -3)(x + -2) = 0 ((-2 * 5 + x * 5) + 3x * (-2 + x)) + (2x + -3)(x + -2) = 0 ((-10 + 5x) + 3x * (-2 + x)) + (2x + -3)(x + -2) = 0 (-10 + 5x + (-2 * 3x + x * 3x)) + (2x + -3)(x + -2) = 0 (-10 + 5x + (-6x + 3x2)) + (2x + -3)(x + -2) = 0 Combine like terms: 5x + -6x = -1x (-10 + -1x + 3x2) + (2x + -3)(x + -2) = 0 Reorder the terms: -10 + -1x + 3x2 + (-3 + 2x)(x + -2) = 0 Reorder the terms: -10 + -1x + 3x2 + (-3 + 2x)(-2 + x) = 0 Multiply (-3 + 2x) * (-2 + x) -10 + -1x + 3x2 + (-3(-2 + x) + 2x * (-2 + x)) = 0 -10 + -1x + 3x2 + ((-2 * -3 + x * -3) + 2x * (-2 + x)) = 0 -10 + -1x + 3x2 + ((6 + -3x) + 2x * (-2 + x)) = 0 -10 + -1x + 3x2 + (6 + -3x + (-2 * 2x + x * 2x)) = 0 -10 + -1x + 3x2 + (6 + -3x + (-4x + 2x2)) = 0 Combine like terms: -3x + -4x = -7x -10 + -1x + 3x2 + (6 + -7x + 2x2) = 0 Reorder the terms: -10 + 6 + -1x + -7x + 3x2 + 2x2 = 0 Combine like terms: -10 + 6 = -4 -4 + -1x + -7x + 3x2 + 2x2 = 0 Combine like terms: -1x + -7x = -8x -4 + -8x + 3x2 + 2x2 = 0 Combine like terms: 3x2 + 2x2 = 5x2 -4 + -8x + 5x2 = 0 Solving -4 + -8x + 5x2 = 0 Solving for variable 'x'. Factor a trinomial. (-2 + -5x)(2 + -1x) = 0Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve: Simplifying -2 + -5x = 0 Solving -2 + -5x = 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 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-0.4, 2}
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