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Simplifying (2x + 1)(x + -3) + -2x(x + -1) = 0 Reorder the terms: (1 + 2x)(x + -3) + -2x(x + -1) = 0 Reorder the terms: (1 + 2x)(-3 + x) + -2x(x + -1) = 0 Multiply (1 + 2x) * (-3 + x) (1(-3 + x) + 2x * (-3 + x)) + -2x(x + -1) = 0 ((-3 * 1 + x * 1) + 2x * (-3 + x)) + -2x(x + -1) = 0 ((-3 + 1x) + 2x * (-3 + x)) + -2x(x + -1) = 0 (-3 + 1x + (-3 * 2x + x * 2x)) + -2x(x + -1) = 0 (-3 + 1x + (-6x + 2x2)) + -2x(x + -1) = 0 Combine like terms: 1x + -6x = -5x (-3 + -5x + 2x2) + -2x(x + -1) = 0 Reorder the terms: -3 + -5x + 2x2 + -2x(-1 + x) = 0 -3 + -5x + 2x2 + (-1 * -2x + x * -2x) = 0 -3 + -5x + 2x2 + (2x + -2x2) = 0 Reorder the terms: -3 + -5x + 2x + 2x2 + -2x2 = 0 Combine like terms: -5x + 2x = -3x -3 + -3x + 2x2 + -2x2 = 0 Combine like terms: 2x2 + -2x2 = 0 -3 + -3x + 0 = 0 -3 + -3x = 0 Solving -3 + -3x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -3x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3x = 0 + 3 -3x = 0 + 3 Combine like terms: 0 + 3 = 3 -3x = 3 Divide each side by '-3'. x = -1 Simplifying x = -1
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