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Simplifying 4x(x + -1) = (2x + 5)(2x + -5) + 1 Reorder the terms: 4x(-1 + x) = (2x + 5)(2x + -5) + 1 (-1 * 4x + x * 4x) = (2x + 5)(2x + -5) + 1 (-4x + 4x2) = (2x + 5)(2x + -5) + 1 Reorder the terms: -4x + 4x2 = (5 + 2x)(2x + -5) + 1 Reorder the terms: -4x + 4x2 = (5 + 2x)(-5 + 2x) + 1 Multiply (5 + 2x) * (-5 + 2x) -4x + 4x2 = (5(-5 + 2x) + 2x * (-5 + 2x)) + 1 -4x + 4x2 = ((-5 * 5 + 2x * 5) + 2x * (-5 + 2x)) + 1 -4x + 4x2 = ((-25 + 10x) + 2x * (-5 + 2x)) + 1 -4x + 4x2 = (-25 + 10x + (-5 * 2x + 2x * 2x)) + 1 -4x + 4x2 = (-25 + 10x + (-10x + 4x2)) + 1 Combine like terms: 10x + -10x = 0 -4x + 4x2 = (-25 + 0 + 4x2) + 1 -4x + 4x2 = (-25 + 4x2) + 1 Reorder the terms: -4x + 4x2 = -25 + 1 + 4x2 Combine like terms: -25 + 1 = -24 -4x + 4x2 = -24 + 4x2 Add '-4x2' to each side of the equation. -4x + 4x2 + -4x2 = -24 + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -4x + 0 = -24 + 4x2 + -4x2 -4x = -24 + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -4x = -24 + 0 -4x = -24 Solving -4x = -24 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Divide each side by '-4'. x = 6 Simplifying x = 6
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