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Simplifying (3v + -12)(12v + -3) = 0 Reorder the terms: (-12 + 3v)(12v + -3) = 0 Reorder the terms: (-12 + 3v)(-3 + 12v) = 0 Multiply (-12 + 3v) * (-3 + 12v) (-12(-3 + 12v) + 3v * (-3 + 12v)) = 0 ((-3 * -12 + 12v * -12) + 3v * (-3 + 12v)) = 0 ((36 + -144v) + 3v * (-3 + 12v)) = 0 (36 + -144v + (-3 * 3v + 12v * 3v)) = 0 (36 + -144v + (-9v + 36v2)) = 0 Combine like terms: -144v + -9v = -153v (36 + -153v + 36v2) = 0 Solving 36 + -153v + 36v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '9'. 9(4 + -17v + 4v2) = 0 Factor a trinomial. 9((1 + -4v)(4 + -1v)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -4v)' equal to zero and attempt to solve: Simplifying 1 + -4v = 0 Solving 1 + -4v = 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 + -4v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4v = 0 + -1 -4v = 0 + -1 Combine like terms: 0 + -1 = -1 -4v = -1 Divide each side by '-4'. v = 0.25 Simplifying v = 0.25Subproblem 2
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 = 4Solution
v = {0.25, 4}
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