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Simplifying x(3x + -2) + x(5x + -1) = (4x + 1)(2x + -3) Reorder the terms: x(-2 + 3x) + x(5x + -1) = (4x + 1)(2x + -3) (-2 * x + 3x * x) + x(5x + -1) = (4x + 1)(2x + -3) (-2x + 3x2) + x(5x + -1) = (4x + 1)(2x + -3) Reorder the terms: -2x + 3x2 + x(-1 + 5x) = (4x + 1)(2x + -3) -2x + 3x2 + (-1 * x + 5x * x) = (4x + 1)(2x + -3) -2x + 3x2 + (-1x + 5x2) = (4x + 1)(2x + -3) Reorder the terms: -2x + -1x + 3x2 + 5x2 = (4x + 1)(2x + -3) Combine like terms: -2x + -1x = -3x -3x + 3x2 + 5x2 = (4x + 1)(2x + -3) Combine like terms: 3x2 + 5x2 = 8x2 -3x + 8x2 = (4x + 1)(2x + -3) Reorder the terms: -3x + 8x2 = (1 + 4x)(2x + -3) Reorder the terms: -3x + 8x2 = (1 + 4x)(-3 + 2x) Multiply (1 + 4x) * (-3 + 2x) -3x + 8x2 = (1(-3 + 2x) + 4x * (-3 + 2x)) -3x + 8x2 = ((-3 * 1 + 2x * 1) + 4x * (-3 + 2x)) -3x + 8x2 = ((-3 + 2x) + 4x * (-3 + 2x)) -3x + 8x2 = (-3 + 2x + (-3 * 4x + 2x * 4x)) -3x + 8x2 = (-3 + 2x + (-12x + 8x2)) Combine like terms: 2x + -12x = -10x -3x + 8x2 = (-3 + -10x + 8x2) Add '-8x2' to each side of the equation. -3x + 8x2 + -8x2 = -3 + -10x + 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -3x + 0 = -3 + -10x + 8x2 + -8x2 -3x = -3 + -10x + 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -3x = -3 + -10x + 0 -3x = -3 + -10x Solving -3x = -3 + -10x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10x' to each side of the equation. -3x + 10x = -3 + -10x + 10x Combine like terms: -3x + 10x = 7x 7x = -3 + -10x + 10x Combine like terms: -10x + 10x = 0 7x = -3 + 0 7x = -3 Divide each side by '7'. x = -0.4285714286 Simplifying x = -0.4285714286
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