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