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Simplifying (3v + 5)(2v + -5) = 0 Reorder the terms: (5 + 3v)(2v + -5) = 0 Reorder the terms: (5 + 3v)(-5 + 2v) = 0 Multiply (5 + 3v) * (-5 + 2v) (5(-5 + 2v) + 3v * (-5 + 2v)) = 0 ((-5 * 5 + 2v * 5) + 3v * (-5 + 2v)) = 0 ((-25 + 10v) + 3v * (-5 + 2v)) = 0 (-25 + 10v + (-5 * 3v + 2v * 3v)) = 0 (-25 + 10v + (-15v + 6v2)) = 0 Combine like terms: 10v + -15v = -5v (-25 + -5v + 6v2) = 0 Solving -25 + -5v + 6v2 = 0 Solving for variable 'v'. Factor a trinomial. (-5 + -3v)(5 + -2v) = 0Subproblem 1
Set the factor '(-5 + -3v)' equal to zero and attempt to solve: Simplifying -5 + -3v = 0 Solving -5 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3v = 0 + 5 -3v = 0 + 5 Combine like terms: 0 + 5 = 5 -3v = 5 Divide each side by '-3'. v = -1.666666667 Simplifying v = -1.666666667Subproblem 2
Set the factor '(5 + -2v)' equal to zero and attempt to solve: Simplifying 5 + -2v = 0 Solving 5 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2v = 0 + -5 -2v = 0 + -5 Combine like terms: 0 + -5 = -5 -2v = -5 Divide each side by '-2'. v = 2.5 Simplifying v = 2.5Solution
v = {-1.666666667, 2.5}
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