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Simplifying 6(v + 4)(2v + -5) = 0 Reorder the terms: 6(4 + v)(2v + -5) = 0 Reorder the terms: 6(4 + v)(-5 + 2v) = 0 Multiply (4 + v) * (-5 + 2v) 6(4(-5 + 2v) + v(-5 + 2v)) = 0 6((-5 * 4 + 2v * 4) + v(-5 + 2v)) = 0 6((-20 + 8v) + v(-5 + 2v)) = 0 6(-20 + 8v + (-5 * v + 2v * v)) = 0 6(-20 + 8v + (-5v + 2v2)) = 0 Combine like terms: 8v + -5v = 3v 6(-20 + 3v + 2v2) = 0 (-20 * 6 + 3v * 6 + 2v2 * 6) = 0 (-120 + 18v + 12v2) = 0 Solving -120 + 18v + 12v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '6'. 6(-20 + 3v + 2v2) = 0 Factor a trinomial. 6((-4 + -1v)(5 + -2v)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + -1v)' equal to zero and attempt to solve: Simplifying -4 + -1v = 0 Solving -4 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1v = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1v = 0 + 4 -1v = 0 + 4 Combine like terms: 0 + 4 = 4 -1v = 4 Divide each side by '-1'. v = -4 Simplifying v = -4Subproblem 2
Set the factor '(5 + -2v)' equal to zero and attempt to solve: Simplifying 5 + -2v = 0 Solving 5 + -2v = 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 + -2v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2v = 0 + -5 -2v = 0 + -5 Combine like terms: 0 + -5 = -5 -2v = -5 Divide each side by '-2'. v = 2.5 Simplifying v = 2.5Solution
v = {-4, 2.5}
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