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Simplifying (4v + -6)(8 + v) = 0 Reorder the terms: (-6 + 4v)(8 + v) = 0 Multiply (-6 + 4v) * (8 + v) (-6(8 + v) + 4v * (8 + v)) = 0 ((8 * -6 + v * -6) + 4v * (8 + v)) = 0 ((-48 + -6v) + 4v * (8 + v)) = 0 (-48 + -6v + (8 * 4v + v * 4v)) = 0 (-48 + -6v + (32v + 4v2)) = 0 Combine like terms: -6v + 32v = 26v (-48 + 26v + 4v2) = 0 Solving -48 + 26v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 13v + 2v2) = 0 Factor a trinomial. 2((-8 + -1v)(3 + -2v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1v)' equal to zero and attempt to solve: Simplifying -8 + -1v = 0 Solving -8 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1v = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1v = 0 + 8 -1v = 0 + 8 Combine like terms: 0 + 8 = 8 -1v = 8 Divide each side by '-1'. v = -8 Simplifying v = -8Subproblem 2
Set the factor '(3 + -2v)' equal to zero and attempt to solve: Simplifying 3 + -2v = 0 Solving 3 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2v = 0 + -3 -2v = 0 + -3 Combine like terms: 0 + -3 = -3 -2v = -3 Divide each side by '-2'. v = 1.5 Simplifying v = 1.5Solution
v = {-8, 1.5}
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