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Simplifying (v + -5)(7v + -35) = 0 Reorder the terms: (-5 + v)(7v + -35) = 0 Reorder the terms: (-5 + v)(-35 + 7v) = 0 Multiply (-5 + v) * (-35 + 7v) (-5(-35 + 7v) + v(-35 + 7v)) = 0 ((-35 * -5 + 7v * -5) + v(-35 + 7v)) = 0 ((175 + -35v) + v(-35 + 7v)) = 0 (175 + -35v + (-35 * v + 7v * v)) = 0 (175 + -35v + (-35v + 7v2)) = 0 Combine like terms: -35v + -35v = -70v (175 + -70v + 7v2) = 0 Solving 175 + -70v + 7v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '7'. 7(25 + -10v + v2) = 0 Factor a trinomial. 7((5 + -1v)(5 + -1v)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Solution
v = {5, 5}
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