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Simplifying (5v + -7)(2v + 9) = 0 Reorder the terms: (-7 + 5v)(2v + 9) = 0 Reorder the terms: (-7 + 5v)(9 + 2v) = 0 Multiply (-7 + 5v) * (9 + 2v) (-7(9 + 2v) + 5v * (9 + 2v)) = 0 ((9 * -7 + 2v * -7) + 5v * (9 + 2v)) = 0 ((-63 + -14v) + 5v * (9 + 2v)) = 0 (-63 + -14v + (9 * 5v + 2v * 5v)) = 0 (-63 + -14v + (45v + 10v2)) = 0 Combine like terms: -14v + 45v = 31v (-63 + 31v + 10v2) = 0 Solving -63 + 31v + 10v2 = 0 Solving for variable 'v'. Factor a trinomial. (-9 + -2v)(7 + -5v) = 0Subproblem 1
Set the factor '(-9 + -2v)' equal to zero and attempt to solve: Simplifying -9 + -2v = 0 Solving -9 + -2v = 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 + -2v = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2v = 0 + 9 -2v = 0 + 9 Combine like terms: 0 + 9 = 9 -2v = 9 Divide each side by '-2'. v = -4.5 Simplifying v = -4.5Subproblem 2
Set the factor '(7 + -5v)' equal to zero and attempt to solve: Simplifying 7 + -5v = 0 Solving 7 + -5v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5v = 0 + -7 -5v = 0 + -7 Combine like terms: 0 + -7 = -7 -5v = -7 Divide each side by '-5'. v = 1.4 Simplifying v = 1.4Solution
v = {-4.5, 1.4}
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