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Simplifying (2 + -2x)(-3x + -2) = (3x + 14)(2x + 7) Reorder the terms: (2 + -2x)(-2 + -3x) = (3x + 14)(2x + 7) Multiply (2 + -2x) * (-2 + -3x) (2(-2 + -3x) + -2x * (-2 + -3x)) = (3x + 14)(2x + 7) ((-2 * 2 + -3x * 2) + -2x * (-2 + -3x)) = (3x + 14)(2x + 7) ((-4 + -6x) + -2x * (-2 + -3x)) = (3x + 14)(2x + 7) (-4 + -6x + (-2 * -2x + -3x * -2x)) = (3x + 14)(2x + 7) (-4 + -6x + (4x + 6x2)) = (3x + 14)(2x + 7) Combine like terms: -6x + 4x = -2x (-4 + -2x + 6x2) = (3x + 14)(2x + 7) Reorder the terms: -4 + -2x + 6x2 = (14 + 3x)(2x + 7) Reorder the terms: -4 + -2x + 6x2 = (14 + 3x)(7 + 2x) Multiply (14 + 3x) * (7 + 2x) -4 + -2x + 6x2 = (14(7 + 2x) + 3x * (7 + 2x)) -4 + -2x + 6x2 = ((7 * 14 + 2x * 14) + 3x * (7 + 2x)) -4 + -2x + 6x2 = ((98 + 28x) + 3x * (7 + 2x)) -4 + -2x + 6x2 = (98 + 28x + (7 * 3x + 2x * 3x)) -4 + -2x + 6x2 = (98 + 28x + (21x + 6x2)) Combine like terms: 28x + 21x = 49x -4 + -2x + 6x2 = (98 + 49x + 6x2) Add '-6x2' to each side of the equation. -4 + -2x + 6x2 + -6x2 = 98 + 49x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + -2x + 0 = 98 + 49x + 6x2 + -6x2 -4 + -2x = 98 + 49x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + -2x = 98 + 49x + 0 -4 + -2x = 98 + 49x Solving -4 + -2x = 98 + 49x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-49x' to each side of the equation. -4 + -2x + -49x = 98 + 49x + -49x Combine like terms: -2x + -49x = -51x -4 + -51x = 98 + 49x + -49x Combine like terms: 49x + -49x = 0 -4 + -51x = 98 + 0 -4 + -51x = 98 Add '4' to each side of the equation. -4 + 4 + -51x = 98 + 4 Combine like terms: -4 + 4 = 0 0 + -51x = 98 + 4 -51x = 98 + 4 Combine like terms: 98 + 4 = 102 -51x = 102 Divide each side by '-51'. x = -2 Simplifying x = -2
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