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Simplifying 12x2 + -7x + -12 = (4x + 3)(3x + 4) Reorder the terms: -12 + -7x + 12x2 = (4x + 3)(3x + 4) Reorder the terms: -12 + -7x + 12x2 = (3 + 4x)(3x + 4) Reorder the terms: -12 + -7x + 12x2 = (3 + 4x)(4 + 3x) Multiply (3 + 4x) * (4 + 3x) -12 + -7x + 12x2 = (3(4 + 3x) + 4x * (4 + 3x)) -12 + -7x + 12x2 = ((4 * 3 + 3x * 3) + 4x * (4 + 3x)) -12 + -7x + 12x2 = ((12 + 9x) + 4x * (4 + 3x)) -12 + -7x + 12x2 = (12 + 9x + (4 * 4x + 3x * 4x)) -12 + -7x + 12x2 = (12 + 9x + (16x + 12x2)) Combine like terms: 9x + 16x = 25x -12 + -7x + 12x2 = (12 + 25x + 12x2) Add '-12x2' to each side of the equation. -12 + -7x + 12x2 + -12x2 = 12 + 25x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -12 + -7x + 0 = 12 + 25x + 12x2 + -12x2 -12 + -7x = 12 + 25x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -12 + -7x = 12 + 25x + 0 -12 + -7x = 12 + 25x Solving -12 + -7x = 12 + 25x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25x' to each side of the equation. -12 + -7x + -25x = 12 + 25x + -25x Combine like terms: -7x + -25x = -32x -12 + -32x = 12 + 25x + -25x Combine like terms: 25x + -25x = 0 -12 + -32x = 12 + 0 -12 + -32x = 12 Add '12' to each side of the equation. -12 + 12 + -32x = 12 + 12 Combine like terms: -12 + 12 = 0 0 + -32x = 12 + 12 -32x = 12 + 12 Combine like terms: 12 + 12 = 24 -32x = 24 Divide each side by '-32'. x = -0.75 Simplifying x = -0.75
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