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Simplifying 4x2 + 12x + 5 = (2x + 5)(2x + 7) Reorder the terms: 5 + 12x + 4x2 = (2x + 5)(2x + 7) Reorder the terms: 5 + 12x + 4x2 = (5 + 2x)(2x + 7) Reorder the terms: 5 + 12x + 4x2 = (5 + 2x)(7 + 2x) Multiply (5 + 2x) * (7 + 2x) 5 + 12x + 4x2 = (5(7 + 2x) + 2x * (7 + 2x)) 5 + 12x + 4x2 = ((7 * 5 + 2x * 5) + 2x * (7 + 2x)) 5 + 12x + 4x2 = ((35 + 10x) + 2x * (7 + 2x)) 5 + 12x + 4x2 = (35 + 10x + (7 * 2x + 2x * 2x)) 5 + 12x + 4x2 = (35 + 10x + (14x + 4x2)) Combine like terms: 10x + 14x = 24x 5 + 12x + 4x2 = (35 + 24x + 4x2) Add '-4x2' to each side of the equation. 5 + 12x + 4x2 + -4x2 = 35 + 24x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 5 + 12x + 0 = 35 + 24x + 4x2 + -4x2 5 + 12x = 35 + 24x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 5 + 12x = 35 + 24x + 0 5 + 12x = 35 + 24x Solving 5 + 12x = 35 + 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. 5 + 12x + -24x = 35 + 24x + -24x Combine like terms: 12x + -24x = -12x 5 + -12x = 35 + 24x + -24x Combine like terms: 24x + -24x = 0 5 + -12x = 35 + 0 5 + -12x = 35 Add '-5' to each side of the equation. 5 + -5 + -12x = 35 + -5 Combine like terms: 5 + -5 = 0 0 + -12x = 35 + -5 -12x = 35 + -5 Combine like terms: 35 + -5 = 30 -12x = 30 Divide each side by '-12'. x = -2.5 Simplifying x = -2.5
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