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Simplifying x(2x + -3) + x(2x + -5) = (4x + 6)(x + -4) Reorder the terms: x(-3 + 2x) + x(2x + -5) = (4x + 6)(x + -4) (-3 * x + 2x * x) + x(2x + -5) = (4x + 6)(x + -4) (-3x + 2x2) + x(2x + -5) = (4x + 6)(x + -4) Reorder the terms: -3x + 2x2 + x(-5 + 2x) = (4x + 6)(x + -4) -3x + 2x2 + (-5 * x + 2x * x) = (4x + 6)(x + -4) -3x + 2x2 + (-5x + 2x2) = (4x + 6)(x + -4) Reorder the terms: -3x + -5x + 2x2 + 2x2 = (4x + 6)(x + -4) Combine like terms: -3x + -5x = -8x -8x + 2x2 + 2x2 = (4x + 6)(x + -4) Combine like terms: 2x2 + 2x2 = 4x2 -8x + 4x2 = (4x + 6)(x + -4) Reorder the terms: -8x + 4x2 = (6 + 4x)(x + -4) Reorder the terms: -8x + 4x2 = (6 + 4x)(-4 + x) Multiply (6 + 4x) * (-4 + x) -8x + 4x2 = (6(-4 + x) + 4x * (-4 + x)) -8x + 4x2 = ((-4 * 6 + x * 6) + 4x * (-4 + x)) -8x + 4x2 = ((-24 + 6x) + 4x * (-4 + x)) -8x + 4x2 = (-24 + 6x + (-4 * 4x + x * 4x)) -8x + 4x2 = (-24 + 6x + (-16x + 4x2)) Combine like terms: 6x + -16x = -10x -8x + 4x2 = (-24 + -10x + 4x2) Add '-4x2' to each side of the equation. -8x + 4x2 + -4x2 = -24 + -10x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -8x + 0 = -24 + -10x + 4x2 + -4x2 -8x = -24 + -10x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -8x = -24 + -10x + 0 -8x = -24 + -10x Solving -8x = -24 + -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. -8x + 10x = -24 + -10x + 10x Combine like terms: -8x + 10x = 2x 2x = -24 + -10x + 10x Combine like terms: -10x + 10x = 0 2x = -24 + 0 2x = -24 Divide each side by '2'. x = -12 Simplifying x = -12
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