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Simplifying (5v + -10)(4v + 3) = 0 Reorder the terms: (-10 + 5v)(4v + 3) = 0 Reorder the terms: (-10 + 5v)(3 + 4v) = 0 Multiply (-10 + 5v) * (3 + 4v) (-10(3 + 4v) + 5v * (3 + 4v)) = 0 ((3 * -10 + 4v * -10) + 5v * (3 + 4v)) = 0 ((-30 + -40v) + 5v * (3 + 4v)) = 0 (-30 + -40v + (3 * 5v + 4v * 5v)) = 0 (-30 + -40v + (15v + 20v2)) = 0 Combine like terms: -40v + 15v = -25v (-30 + -25v + 20v2) = 0 Solving -30 + -25v + 20v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + -5v + 4v2) = 0 Factor a trinomial. 5((-3 + -4v)(2 + -1v)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -4v)' equal to zero and attempt to solve: Simplifying -3 + -4v = 0 Solving -3 + -4v = 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 + -4v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4v = 0 + 3 -4v = 0 + 3 Combine like terms: 0 + 3 = 3 -4v = 3 Divide each side by '-4'. v = -0.75 Simplifying v = -0.75Subproblem 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 = {-0.75, 2}
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