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Simplifying 150 = (2x + 15)(2x + 10) Reorder the terms: 150 = (15 + 2x)(2x + 10) Reorder the terms: 150 = (15 + 2x)(10 + 2x) Multiply (15 + 2x) * (10 + 2x) 150 = (15(10 + 2x) + 2x * (10 + 2x)) 150 = ((10 * 15 + 2x * 15) + 2x * (10 + 2x)) 150 = ((150 + 30x) + 2x * (10 + 2x)) 150 = (150 + 30x + (10 * 2x + 2x * 2x)) 150 = (150 + 30x + (20x + 4x2)) Combine like terms: 30x + 20x = 50x 150 = (150 + 50x + 4x2) Add '-150' to each side of the equation. 150 + -150 = 150 + 50x + -150 + 4x2 Combine like terms: 150 + -150 = 0 0 = 150 + 50x + -150 + 4x2 Reorder the terms: 0 = 150 + -150 + 50x + 4x2 Combine like terms: 150 + -150 = 0 0 = 0 + 50x + 4x2 0 = 50x + 4x2 Solving 0 = 50x + 4x2 Solving for variable 'x'. Remove the zero: -50x + -4x2 = 50x + 4x2 + -50x + -4x2 Reorder the terms: -50x + -4x2 = 50x + -50x + 4x2 + -4x2 Combine like terms: 50x + -50x = 0 -50x + -4x2 = 0 + 4x2 + -4x2 -50x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -50x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2x'. -2x(25 + 2x) = 0 Ignore the factor -2.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 + 2x)' equal to zero and attempt to solve: Simplifying 25 + 2x = 0 Solving 25 + 2x = 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 + 2x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 2x = 0 + -25 2x = 0 + -25 Combine like terms: 0 + -25 = -25 2x = -25 Divide each side by '2'. x = -12.5 Simplifying x = -12.5Solution
x = {0, -12.5}
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