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Simplifying (x + -5)(2x + 3) + -2x(x + 1) = 0 Reorder the terms: (-5 + x)(2x + 3) + -2x(x + 1) = 0 Reorder the terms: (-5 + x)(3 + 2x) + -2x(x + 1) = 0 Multiply (-5 + x) * (3 + 2x) (-5(3 + 2x) + x(3 + 2x)) + -2x(x + 1) = 0 ((3 * -5 + 2x * -5) + x(3 + 2x)) + -2x(x + 1) = 0 ((-15 + -10x) + x(3 + 2x)) + -2x(x + 1) = 0 (-15 + -10x + (3 * x + 2x * x)) + -2x(x + 1) = 0 (-15 + -10x + (3x + 2x2)) + -2x(x + 1) = 0 Combine like terms: -10x + 3x = -7x (-15 + -7x + 2x2) + -2x(x + 1) = 0 Reorder the terms: -15 + -7x + 2x2 + -2x(1 + x) = 0 -15 + -7x + 2x2 + (1 * -2x + x * -2x) = 0 -15 + -7x + 2x2 + (-2x + -2x2) = 0 Reorder the terms: -15 + -7x + -2x + 2x2 + -2x2 = 0 Combine like terms: -7x + -2x = -9x -15 + -9x + 2x2 + -2x2 = 0 Combine like terms: 2x2 + -2x2 = 0 -15 + -9x + 0 = 0 -15 + -9x = 0 Solving -15 + -9x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -9x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -9x = 0 + 15 -9x = 0 + 15 Combine like terms: 0 + 15 = 15 -9x = 15 Divide each side by '-9'. x = -1.666666667 Simplifying x = -1.666666667
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