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Simplifying (225 + -5x)(75 + -1x) = 0 Multiply (225 + -5x) * (75 + -1x) (225(75 + -1x) + -5x * (75 + -1x)) = 0 ((75 * 225 + -1x * 225) + -5x * (75 + -1x)) = 0 ((16875 + -225x) + -5x * (75 + -1x)) = 0 (16875 + -225x + (75 * -5x + -1x * -5x)) = 0 (16875 + -225x + (-375x + 5x2)) = 0 Combine like terms: -225x + -375x = -600x (16875 + -600x + 5x2) = 0 Solving 16875 + -600x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(3375 + -120x + x2) = 0 Factor a trinomial. 5((45 + -1x)(75 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(45 + -1x)' equal to zero and attempt to solve: Simplifying 45 + -1x = 0 Solving 45 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + -1x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -1x = 0 + -45 -1x = 0 + -45 Combine like terms: 0 + -45 = -45 -1x = -45 Divide each side by '-1'. x = 45 Simplifying x = 45Subproblem 2
Set the factor '(75 + -1x)' equal to zero and attempt to solve: Simplifying 75 + -1x = 0 Solving 75 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + -1x = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -1x = 0 + -75 -1x = 0 + -75 Combine like terms: 0 + -75 = -75 -1x = -75 Divide each side by '-1'. x = 75 Simplifying x = 75Solution
x = {45, 75}
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