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Simplifying (9 + v)(4v + -6) = 0 Reorder the terms: (9 + v)(-6 + 4v) = 0 Multiply (9 + v) * (-6 + 4v) (9(-6 + 4v) + v(-6 + 4v)) = 0 ((-6 * 9 + 4v * 9) + v(-6 + 4v)) = 0 ((-54 + 36v) + v(-6 + 4v)) = 0 (-54 + 36v + (-6 * v + 4v * v)) = 0 (-54 + 36v + (-6v + 4v2)) = 0 Combine like terms: 36v + -6v = 30v (-54 + 30v + 4v2) = 0 Solving -54 + 30v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 15v + 2v2) = 0 Factor a trinomial. 2((-9 + -1v)(3 + -2v)) = 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 '(3 + -2v)' equal to zero and attempt to solve: Simplifying 3 + -2v = 0 Solving 3 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2v = 0 + -3 -2v = 0 + -3 Combine like terms: 0 + -3 = -3 -2v = -3 Divide each side by '-2'. v = 1.5 Simplifying v = 1.5Solution
v = {-9, 1.5}
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