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Simplifying -3(v + 5)(v + 2) = 0 Reorder the terms: -3(5 + v)(v + 2) = 0 Reorder the terms: -3(5 + v)(2 + v) = 0 Multiply (5 + v) * (2 + v) -3(5(2 + v) + v(2 + v)) = 0 -3((2 * 5 + v * 5) + v(2 + v)) = 0 -3((10 + 5v) + v(2 + v)) = 0 -3(10 + 5v + (2 * v + v * v)) = 0 -3(10 + 5v + (2v + v2)) = 0 Combine like terms: 5v + 2v = 7v -3(10 + 7v + v2) = 0 (10 * -3 + 7v * -3 + v2 * -3) = 0 (-30 + -21v + -3v2) = 0 Solving -30 + -21v + -3v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '-3'. -3(10 + 7v + v2) = 0 Factor a trinomial. -3((5 + v)(2 + v)) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve: Simplifying 5 + v = 0 Solving 5 + v = 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 + v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + v = 0 + -5 v = 0 + -5 Combine like terms: 0 + -5 = -5 v = -5 Simplifying v = -5Subproblem 2
Set the factor '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2Solution
v = {-5, -2}
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