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Simplifying (2x + -3)(-1x + -2) = (x + 1)(2x + -3) Reorder the terms: (-3 + 2x)(-1x + -2) = (x + 1)(2x + -3) Reorder the terms: (-3 + 2x)(-2 + -1x) = (x + 1)(2x + -3) Multiply (-3 + 2x) * (-2 + -1x) (-3(-2 + -1x) + 2x * (-2 + -1x)) = (x + 1)(2x + -3) ((-2 * -3 + -1x * -3) + 2x * (-2 + -1x)) = (x + 1)(2x + -3) ((6 + 3x) + 2x * (-2 + -1x)) = (x + 1)(2x + -3) (6 + 3x + (-2 * 2x + -1x * 2x)) = (x + 1)(2x + -3) (6 + 3x + (-4x + -2x2)) = (x + 1)(2x + -3) Combine like terms: 3x + -4x = -1x (6 + -1x + -2x2) = (x + 1)(2x + -3) Reorder the terms: 6 + -1x + -2x2 = (1 + x)(2x + -3) Reorder the terms: 6 + -1x + -2x2 = (1 + x)(-3 + 2x) Multiply (1 + x) * (-3 + 2x) 6 + -1x + -2x2 = (1(-3 + 2x) + x(-3 + 2x)) 6 + -1x + -2x2 = ((-3 * 1 + 2x * 1) + x(-3 + 2x)) 6 + -1x + -2x2 = ((-3 + 2x) + x(-3 + 2x)) 6 + -1x + -2x2 = (-3 + 2x + (-3 * x + 2x * x)) 6 + -1x + -2x2 = (-3 + 2x + (-3x + 2x2)) Combine like terms: 2x + -3x = -1x 6 + -1x + -2x2 = (-3 + -1x + 2x2) Add 'x' to each side of the equation. 6 + -1x + x + -2x2 = -3 + -1x + x + 2x2 Combine like terms: -1x + x = 0 6 + 0 + -2x2 = -3 + -1x + x + 2x2 6 + -2x2 = -3 + -1x + x + 2x2 Combine like terms: -1x + x = 0 6 + -2x2 = -3 + 0 + 2x2 6 + -2x2 = -3 + 2x2 Solving 6 + -2x2 = -3 + 2x2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x2' to each side of the equation. 6 + -2x2 + -2x2 = -3 + 2x2 + -2x2 Combine like terms: -2x2 + -2x2 = -4x2 6 + -4x2 = -3 + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 6 + -4x2 = -3 + 0 6 + -4x2 = -3 Add '-6' to each side of the equation. 6 + -6 + -4x2 = -3 + -6 Combine like terms: 6 + -6 = 0 0 + -4x2 = -3 + -6 -4x2 = -3 + -6 Combine like terms: -3 + -6 = -9 -4x2 = -9 Divide each side by '-4'. x2 = 2.25 Simplifying x2 = 2.25 Take the square root of each side: x = {-1.5, 1.5}
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