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Simplifying (v + -6)(v + -6) = 2(v + -6)(v + -5) Reorder the terms: (-6 + v)(v + -6) = 2(v + -6)(v + -5) Reorder the terms: (-6 + v)(-6 + v) = 2(v + -6)(v + -5) Multiply (-6 + v) * (-6 + v) (-6(-6 + v) + v(-6 + v)) = 2(v + -6)(v + -5) ((-6 * -6 + v * -6) + v(-6 + v)) = 2(v + -6)(v + -5) ((36 + -6v) + v(-6 + v)) = 2(v + -6)(v + -5) (36 + -6v + (-6 * v + v * v)) = 2(v + -6)(v + -5) (36 + -6v + (-6v + v2)) = 2(v + -6)(v + -5) Combine like terms: -6v + -6v = -12v (36 + -12v + v2) = 2(v + -6)(v + -5) Reorder the terms: 36 + -12v + v2 = 2(-6 + v)(v + -5) Reorder the terms: 36 + -12v + v2 = 2(-6 + v)(-5 + v) Multiply (-6 + v) * (-5 + v) 36 + -12v + v2 = 2(-6(-5 + v) + v(-5 + v)) 36 + -12v + v2 = 2((-5 * -6 + v * -6) + v(-5 + v)) 36 + -12v + v2 = 2((30 + -6v) + v(-5 + v)) 36 + -12v + v2 = 2(30 + -6v + (-5 * v + v * v)) 36 + -12v + v2 = 2(30 + -6v + (-5v + v2)) Combine like terms: -6v + -5v = -11v 36 + -12v + v2 = 2(30 + -11v + v2) 36 + -12v + v2 = (30 * 2 + -11v * 2 + v2 * 2) 36 + -12v + v2 = (60 + -22v + 2v2) Solving 36 + -12v + v2 = 60 + -22v + 2v2 Solving for variable 'v'. Reorder the terms: 36 + -60 + -12v + 22v + v2 + -2v2 = 60 + -22v + 2v2 + -60 + 22v + -2v2 Combine like terms: 36 + -60 = -24 -24 + -12v + 22v + v2 + -2v2 = 60 + -22v + 2v2 + -60 + 22v + -2v2 Combine like terms: -12v + 22v = 10v -24 + 10v + v2 + -2v2 = 60 + -22v + 2v2 + -60 + 22v + -2v2 Combine like terms: v2 + -2v2 = -1v2 -24 + 10v + -1v2 = 60 + -22v + 2v2 + -60 + 22v + -2v2 Reorder the terms: -24 + 10v + -1v2 = 60 + -60 + -22v + 22v + 2v2 + -2v2 Combine like terms: 60 + -60 = 0 -24 + 10v + -1v2 = 0 + -22v + 22v + 2v2 + -2v2 -24 + 10v + -1v2 = -22v + 22v + 2v2 + -2v2 Combine like terms: -22v + 22v = 0 -24 + 10v + -1v2 = 0 + 2v2 + -2v2 -24 + 10v + -1v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 -24 + 10v + -1v2 = 0 Factor a trinomial. (-6 + v)(4 + -1v) = 0Subproblem 1
Set the factor '(-6 + v)' equal to zero and attempt to solve: Simplifying -6 + v = 0 Solving -6 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + v = 0 + 6 Combine like terms: -6 + 6 = 0 0 + v = 0 + 6 v = 0 + 6 Combine like terms: 0 + 6 = 6 v = 6 Simplifying v = 6Subproblem 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 = {6, 4}
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