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Simplifying (8v + 4)(5v + 2) = 0 Reorder the terms: (4 + 8v)(5v + 2) = 0 Reorder the terms: (4 + 8v)(2 + 5v) = 0 Multiply (4 + 8v) * (2 + 5v) (4(2 + 5v) + 8v * (2 + 5v)) = 0 ((2 * 4 + 5v * 4) + 8v * (2 + 5v)) = 0 ((8 + 20v) + 8v * (2 + 5v)) = 0 (8 + 20v + (2 * 8v + 5v * 8v)) = 0 (8 + 20v + (16v + 40v2)) = 0 Combine like terms: 20v + 16v = 36v (8 + 36v + 40v2) = 0 Solving 8 + 36v + 40v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + 9v + 10v2) = 0 Factor a trinomial. 4((1 + 2v)(2 + 5v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 2v)' equal to zero and attempt to solve: Simplifying 1 + 2v = 0 Solving 1 + 2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2v = 0 + -1 2v = 0 + -1 Combine like terms: 0 + -1 = -1 2v = -1 Divide each side by '2'. v = -0.5 Simplifying v = -0.5Subproblem 2
Set the factor '(2 + 5v)' equal to zero and attempt to solve: Simplifying 2 + 5v = 0 Solving 2 + 5v = 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 + 5v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5v = 0 + -2 5v = 0 + -2 Combine like terms: 0 + -2 = -2 5v = -2 Divide each side by '5'. v = -0.4 Simplifying v = -0.4Solution
v = {-0.5, -0.4}
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