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Simplifying 12x + -1(2x + 3)(2x + 3) = 8x + -1(2x + -5)(2x + -3) Reorder the terms: 12x + -1(3 + 2x)(2x + 3) = 8x + -1(2x + -5)(2x + -3) Reorder the terms: 12x + -1(3 + 2x)(3 + 2x) = 8x + -1(2x + -5)(2x + -3) Multiply (3 + 2x) * (3 + 2x) 12x + -1(3(3 + 2x) + 2x * (3 + 2x)) = 8x + -1(2x + -5)(2x + -3) 12x + -1((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 8x + -1(2x + -5)(2x + -3) 12x + -1((9 + 6x) + 2x * (3 + 2x)) = 8x + -1(2x + -5)(2x + -3) 12x + -1(9 + 6x + (3 * 2x + 2x * 2x)) = 8x + -1(2x + -5)(2x + -3) 12x + -1(9 + 6x + (6x + 4x2)) = 8x + -1(2x + -5)(2x + -3) Combine like terms: 6x + 6x = 12x 12x + -1(9 + 12x + 4x2) = 8x + -1(2x + -5)(2x + -3) 12x + (9 * -1 + 12x * -1 + 4x2 * -1) = 8x + -1(2x + -5)(2x + -3) 12x + (-9 + -12x + -4x2) = 8x + -1(2x + -5)(2x + -3) Reorder the terms: -9 + 12x + -12x + -4x2 = 8x + -1(2x + -5)(2x + -3) Combine like terms: 12x + -12x = 0 -9 + 0 + -4x2 = 8x + -1(2x + -5)(2x + -3) -9 + -4x2 = 8x + -1(2x + -5)(2x + -3) Reorder the terms: -9 + -4x2 = 8x + -1(-5 + 2x)(2x + -3) Reorder the terms: -9 + -4x2 = 8x + -1(-5 + 2x)(-3 + 2x) Multiply (-5 + 2x) * (-3 + 2x) -9 + -4x2 = 8x + -1(-5(-3 + 2x) + 2x * (-3 + 2x)) -9 + -4x2 = 8x + -1((-3 * -5 + 2x * -5) + 2x * (-3 + 2x)) -9 + -4x2 = 8x + -1((15 + -10x) + 2x * (-3 + 2x)) -9 + -4x2 = 8x + -1(15 + -10x + (-3 * 2x + 2x * 2x)) -9 + -4x2 = 8x + -1(15 + -10x + (-6x + 4x2)) Combine like terms: -10x + -6x = -16x -9 + -4x2 = 8x + -1(15 + -16x + 4x2) -9 + -4x2 = 8x + (15 * -1 + -16x * -1 + 4x2 * -1) -9 + -4x2 = 8x + (-15 + 16x + -4x2) Reorder the terms: -9 + -4x2 = -15 + 8x + 16x + -4x2 Combine like terms: 8x + 16x = 24x -9 + -4x2 = -15 + 24x + -4x2 Add '4x2' to each side of the equation. -9 + -4x2 + 4x2 = -15 + 24x + -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -9 + 0 = -15 + 24x + -4x2 + 4x2 -9 = -15 + 24x + -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -9 = -15 + 24x + 0 -9 = -15 + 24x Solving -9 = -15 + 24x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24x' to each side of the equation. -9 + -24x = -15 + 24x + -24x Combine like terms: 24x + -24x = 0 -9 + -24x = -15 + 0 -9 + -24x = -15 Add '9' to each side of the equation. -9 + 9 + -24x = -15 + 9 Combine like terms: -9 + 9 = 0 0 + -24x = -15 + 9 -24x = -15 + 9 Combine like terms: -15 + 9 = -6 -24x = -6 Divide each side by '-24'. x = 0.25 Simplifying x = 0.25
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