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Simplifying 50x3 + 100x2 + 48 = 2x(5x + 4)(5x + 6) Reorder the terms: 48 + 100x2 + 50x3 = 2x(5x + 4)(5x + 6) Reorder the terms: 48 + 100x2 + 50x3 = 2x(4 + 5x)(5x + 6) Reorder the terms: 48 + 100x2 + 50x3 = 2x(4 + 5x)(6 + 5x) Multiply (4 + 5x) * (6 + 5x) 48 + 100x2 + 50x3 = 2x(4(6 + 5x) + 5x * (6 + 5x)) 48 + 100x2 + 50x3 = 2x((6 * 4 + 5x * 4) + 5x * (6 + 5x)) 48 + 100x2 + 50x3 = 2x((24 + 20x) + 5x * (6 + 5x)) 48 + 100x2 + 50x3 = 2x(24 + 20x + (6 * 5x + 5x * 5x)) 48 + 100x2 + 50x3 = 2x(24 + 20x + (30x + 25x2)) Combine like terms: 20x + 30x = 50x 48 + 100x2 + 50x3 = 2x(24 + 50x + 25x2) 48 + 100x2 + 50x3 = (24 * 2x + 50x * 2x + 25x2 * 2x) 48 + 100x2 + 50x3 = (48x + 100x2 + 50x3) Add '-100x2' to each side of the equation. 48 + 100x2 + -100x2 + 50x3 = 48x + 100x2 + -100x2 + 50x3 Combine like terms: 100x2 + -100x2 = 0 48 + 0 + 50x3 = 48x + 100x2 + -100x2 + 50x3 48 + 50x3 = 48x + 100x2 + -100x2 + 50x3 Combine like terms: 100x2 + -100x2 = 0 48 + 50x3 = 48x + 0 + 50x3 48 + 50x3 = 48x + 50x3 Add '-50x3' to each side of the equation. 48 + 50x3 + -50x3 = 48x + 50x3 + -50x3 Combine like terms: 50x3 + -50x3 = 0 48 + 0 = 48x + 50x3 + -50x3 48 = 48x + 50x3 + -50x3 Combine like terms: 50x3 + -50x3 = 0 48 = 48x + 0 48 = 48x Solving 48 = 48x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-48x' to each side of the equation. 48 + -48x = 48x + -48x Combine like terms: 48x + -48x = 0 48 + -48x = 0 Add '-48' to each side of the equation. 48 + -48 + -48x = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -48x = 0 + -48 -48x = 0 + -48 Combine like terms: 0 + -48 = -48 -48x = -48 Divide each side by '-48'. x = 1 Simplifying x = 1
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