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Simplifying x(2x + -2) + x(2x + -6) = (4x + 7)(x + -3) Reorder the terms: x(-2 + 2x) + x(2x + -6) = (4x + 7)(x + -3) (-2 * x + 2x * x) + x(2x + -6) = (4x + 7)(x + -3) (-2x + 2x2) + x(2x + -6) = (4x + 7)(x + -3) Reorder the terms: -2x + 2x2 + x(-6 + 2x) = (4x + 7)(x + -3) -2x + 2x2 + (-6 * x + 2x * x) = (4x + 7)(x + -3) -2x + 2x2 + (-6x + 2x2) = (4x + 7)(x + -3) Reorder the terms: -2x + -6x + 2x2 + 2x2 = (4x + 7)(x + -3) Combine like terms: -2x + -6x = -8x -8x + 2x2 + 2x2 = (4x + 7)(x + -3) Combine like terms: 2x2 + 2x2 = 4x2 -8x + 4x2 = (4x + 7)(x + -3) Reorder the terms: -8x + 4x2 = (7 + 4x)(x + -3) Reorder the terms: -8x + 4x2 = (7 + 4x)(-3 + x) Multiply (7 + 4x) * (-3 + x) -8x + 4x2 = (7(-3 + x) + 4x * (-3 + x)) -8x + 4x2 = ((-3 * 7 + x * 7) + 4x * (-3 + x)) -8x + 4x2 = ((-21 + 7x) + 4x * (-3 + x)) -8x + 4x2 = (-21 + 7x + (-3 * 4x + x * 4x)) -8x + 4x2 = (-21 + 7x + (-12x + 4x2)) Combine like terms: 7x + -12x = -5x -8x + 4x2 = (-21 + -5x + 4x2) Add '-4x2' to each side of the equation. -8x + 4x2 + -4x2 = -21 + -5x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -8x + 0 = -21 + -5x + 4x2 + -4x2 -8x = -21 + -5x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -8x = -21 + -5x + 0 -8x = -21 + -5x Solving -8x = -21 + -5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5x' to each side of the equation. -8x + 5x = -21 + -5x + 5x Combine like terms: -8x + 5x = -3x -3x = -21 + -5x + 5x Combine like terms: -5x + 5x = 0 -3x = -21 + 0 -3x = -21 Divide each side by '-3'. x = 7 Simplifying x = 7
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