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Simplifying (5x + -25)(7x + 21) = 0 Reorder the terms: (-25 + 5x)(7x + 21) = 0 Reorder the terms: (-25 + 5x)(21 + 7x) = 0 Multiply (-25 + 5x) * (21 + 7x) (-25(21 + 7x) + 5x * (21 + 7x)) = 0 ((21 * -25 + 7x * -25) + 5x * (21 + 7x)) = 0 ((-525 + -175x) + 5x * (21 + 7x)) = 0 (-525 + -175x + (21 * 5x + 7x * 5x)) = 0 (-525 + -175x + (105x + 35x2)) = 0 Combine like terms: -175x + 105x = -70x (-525 + -70x + 35x2) = 0 Solving -525 + -70x + 35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '35'. 35(-15 + -2x + x2) = 0 Factor a trinomial. 35((-3 + -1x)(5 + -1x)) = 0 Ignore the factor 35.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-3, 5}
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