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Simplifying x(2x + -2) + x(5x + -5) = (7x + 7)(x + -4) Reorder the terms: x(-2 + 2x) + x(5x + -5) = (7x + 7)(x + -4) (-2 * x + 2x * x) + x(5x + -5) = (7x + 7)(x + -4) (-2x + 2x2) + x(5x + -5) = (7x + 7)(x + -4) Reorder the terms: -2x + 2x2 + x(-5 + 5x) = (7x + 7)(x + -4) -2x + 2x2 + (-5 * x + 5x * x) = (7x + 7)(x + -4) -2x + 2x2 + (-5x + 5x2) = (7x + 7)(x + -4) Reorder the terms: -2x + -5x + 2x2 + 5x2 = (7x + 7)(x + -4) Combine like terms: -2x + -5x = -7x -7x + 2x2 + 5x2 = (7x + 7)(x + -4) Combine like terms: 2x2 + 5x2 = 7x2 -7x + 7x2 = (7x + 7)(x + -4) Reorder the terms: -7x + 7x2 = (7 + 7x)(x + -4) Reorder the terms: -7x + 7x2 = (7 + 7x)(-4 + x) Multiply (7 + 7x) * (-4 + x) -7x + 7x2 = (7(-4 + x) + 7x * (-4 + x)) -7x + 7x2 = ((-4 * 7 + x * 7) + 7x * (-4 + x)) -7x + 7x2 = ((-28 + 7x) + 7x * (-4 + x)) -7x + 7x2 = (-28 + 7x + (-4 * 7x + x * 7x)) -7x + 7x2 = (-28 + 7x + (-28x + 7x2)) Combine like terms: 7x + -28x = -21x -7x + 7x2 = (-28 + -21x + 7x2) Add '-7x2' to each side of the equation. -7x + 7x2 + -7x2 = -28 + -21x + 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -7x + 0 = -28 + -21x + 7x2 + -7x2 -7x = -28 + -21x + 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -7x = -28 + -21x + 0 -7x = -28 + -21x Solving -7x = -28 + -21x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21x' to each side of the equation. -7x + 21x = -28 + -21x + 21x Combine like terms: -7x + 21x = 14x 14x = -28 + -21x + 21x Combine like terms: -21x + 21x = 0 14x = -28 + 0 14x = -28 Divide each side by '14'. x = -2 Simplifying x = -2
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