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Simplifying (5v + 3)(2v + -6) = 0 Reorder the terms: (3 + 5v)(2v + -6) = 0 Reorder the terms: (3 + 5v)(-6 + 2v) = 0 Multiply (3 + 5v) * (-6 + 2v) (3(-6 + 2v) + 5v * (-6 + 2v)) = 0 ((-6 * 3 + 2v * 3) + 5v * (-6 + 2v)) = 0 ((-18 + 6v) + 5v * (-6 + 2v)) = 0 (-18 + 6v + (-6 * 5v + 2v * 5v)) = 0 (-18 + 6v + (-30v + 10v2)) = 0 Combine like terms: 6v + -30v = -24v (-18 + -24v + 10v2) = 0 Solving -18 + -24v + 10v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -12v + 5v2) = 0 Factor a trinomial. 2((-3 + -5v)(3 + -1v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -5v)' equal to zero and attempt to solve: Simplifying -3 + -5v = 0 Solving -3 + -5v = 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 + -5v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5v = 0 + 3 -5v = 0 + 3 Combine like terms: 0 + 3 = 3 -5v = 3 Divide each side by '-5'. v = -0.6 Simplifying v = -0.6Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 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 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Solution
v = {-0.6, 3}
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