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Simplifying 4(v + -3) + -6 = -2v(v + 6) Reorder the terms: 4(-3 + v) + -6 = -2v(v + 6) (-3 * 4 + v * 4) + -6 = -2v(v + 6) (-12 + 4v) + -6 = -2v(v + 6) Reorder the terms: -12 + -6 + 4v = -2v(v + 6) Combine like terms: -12 + -6 = -18 -18 + 4v = -2v(v + 6) Reorder the terms: -18 + 4v = -2v(6 + v) -18 + 4v = (6 * -2v + v * -2v) -18 + 4v = (-12v + -2v2) Solving -18 + 4v = -12v + -2v2 Solving for variable 'v'. Combine like terms: 4v + 12v = 16v -18 + 16v + 2v2 = -12v + -2v2 + 12v + 2v2 Reorder the terms: -18 + 16v + 2v2 = -12v + 12v + -2v2 + 2v2 Combine like terms: -12v + 12v = 0 -18 + 16v + 2v2 = 0 + -2v2 + 2v2 -18 + 16v + 2v2 = -2v2 + 2v2 Combine like terms: -2v2 + 2v2 = 0 -18 + 16v + 2v2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 8v + v2) = 0 Factor a trinomial. 2((-9 + -1v)(1 + -1v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -1v)' equal to zero and attempt to solve: Simplifying -9 + -1v = 0 Solving -9 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1v = 0 + 9 -1v = 0 + 9 Combine like terms: 0 + 9 = 9 -1v = 9 Divide each side by '-1'. v = -9 Simplifying v = -9Subproblem 2
Set the factor '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 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 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1Solution
v = {-9, 1}
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