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Simplifying 4(x + -15)(x + 15) = 20(x + 15) + 16(5)(x + -15) Reorder the terms: 4(-15 + x)(x + 15) = 20(x + 15) + 16(5)(x + -15) Reorder the terms: 4(-15 + x)(15 + x) = 20(x + 15) + 16(5)(x + -15) Multiply (-15 + x) * (15 + x) 4(-15(15 + x) + x(15 + x)) = 20(x + 15) + 16(5)(x + -15) 4((15 * -15 + x * -15) + x(15 + x)) = 20(x + 15) + 16(5)(x + -15) 4((-225 + -15x) + x(15 + x)) = 20(x + 15) + 16(5)(x + -15) 4(-225 + -15x + (15 * x + x * x)) = 20(x + 15) + 16(5)(x + -15) 4(-225 + -15x + (15x + x2)) = 20(x + 15) + 16(5)(x + -15) Combine like terms: -15x + 15x = 0 4(-225 + 0 + x2) = 20(x + 15) + 16(5)(x + -15) 4(-225 + x2) = 20(x + 15) + 16(5)(x + -15) (-225 * 4 + x2 * 4) = 20(x + 15) + 16(5)(x + -15) (-900 + 4x2) = 20(x + 15) + 16(5)(x + -15) Reorder the terms: -900 + 4x2 = 20(15 + x) + 16(5)(x + -15) -900 + 4x2 = (15 * 20 + x * 20) + 16(5)(x + -15) -900 + 4x2 = (300 + 20x) + 16(5)(x + -15) Reorder the terms: -900 + 4x2 = 300 + 20x + 16 * 5(-15 + x) Multiply 16 * 5 -900 + 4x2 = 300 + 20x + 80(-15 + x) -900 + 4x2 = 300 + 20x + (-15 * 80 + x * 80) -900 + 4x2 = 300 + 20x + (-1200 + 80x) Reorder the terms: -900 + 4x2 = 300 + -1200 + 20x + 80x Combine like terms: 300 + -1200 = -900 -900 + 4x2 = -900 + 20x + 80x Combine like terms: 20x + 80x = 100x -900 + 4x2 = -900 + 100x Add '900' to each side of the equation. -900 + 900 + 4x2 = -900 + 900 + 100x Combine like terms: -900 + 900 = 0 0 + 4x2 = -900 + 900 + 100x 4x2 = -900 + 900 + 100x Combine like terms: -900 + 900 = 0 4x2 = 0 + 100x 4x2 = 100x Solving 4x2 = 100x Solving for variable 'x'. Reorder the terms: -100x + 4x2 = 100x + -100x Combine like terms: 100x + -100x = 0 -100x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4x'. 4x(-25 + x) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-25 + x)' equal to zero and attempt to solve: Simplifying -25 + x = 0 Solving -25 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + x = 0 + 25 x = 0 + 25 Combine like terms: 0 + 25 = 25 x = 25 Simplifying x = 25Solution
x = {0, 25}
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