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Simplifying 0 = (30 + 5x)(50 + -1x) Multiply (30 + 5x) * (50 + -1x) 0 = (30(50 + -1x) + 5x * (50 + -1x)) 0 = ((50 * 30 + -1x * 30) + 5x * (50 + -1x)) 0 = ((1500 + -30x) + 5x * (50 + -1x)) 0 = (1500 + -30x + (50 * 5x + -1x * 5x)) 0 = (1500 + -30x + (250x + -5x2)) Combine like terms: -30x + 250x = 220x 0 = (1500 + 220x + -5x2) Solving 0 = 1500 + 220x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -1500 = -1500 -1500 + -220x + 5x2 = 1500 + 220x + -5x2 + -1500 + -220x + 5x2 Reorder the terms: -1500 + -220x + 5x2 = 1500 + -1500 + 220x + -220x + -5x2 + 5x2 Combine like terms: 1500 + -1500 = 0 -1500 + -220x + 5x2 = 0 + 220x + -220x + -5x2 + 5x2 -1500 + -220x + 5x2 = 220x + -220x + -5x2 + 5x2 Combine like terms: 220x + -220x = 0 -1500 + -220x + 5x2 = 0 + -5x2 + 5x2 -1500 + -220x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -1500 + -220x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-300 + -44x + x2) = 0 Factor a trinomial. 5((-6 + -1x)(50 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(50 + -1x)' equal to zero and attempt to solve: Simplifying 50 + -1x = 0 Solving 50 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x = 0 + -50 -1x = 0 + -50 Combine like terms: 0 + -50 = -50 -1x = -50 Divide each side by '-1'. x = 50 Simplifying x = 50Solution
x = {-6, 50}
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