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Simplifying (5v + -2)(6v + -4) = 0 Reorder the terms: (-2 + 5v)(6v + -4) = 0 Reorder the terms: (-2 + 5v)(-4 + 6v) = 0 Multiply (-2 + 5v) * (-4 + 6v) (-2(-4 + 6v) + 5v * (-4 + 6v)) = 0 ((-4 * -2 + 6v * -2) + 5v * (-4 + 6v)) = 0 ((8 + -12v) + 5v * (-4 + 6v)) = 0 (8 + -12v + (-4 * 5v + 6v * 5v)) = 0 (8 + -12v + (-20v + 30v2)) = 0 Combine like terms: -12v + -20v = -32v (8 + -32v + 30v2) = 0 Solving 8 + -32v + 30v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -16v + 15v2) = 0 Factor a trinomial. 2((2 + -5v)(2 + -3v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -5v)' equal to zero and attempt to solve: Simplifying 2 + -5v = 0 Solving 2 + -5v = 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 + -5v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5v = 0 + -2 -5v = 0 + -2 Combine like terms: 0 + -2 = -2 -5v = -2 Divide each side by '-5'. v = 0.4 Simplifying v = 0.4Subproblem 2
Set the factor '(2 + -3v)' equal to zero and attempt to solve: Simplifying 2 + -3v = 0 Solving 2 + -3v = 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 + -3v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3v = 0 + -2 -3v = 0 + -2 Combine like terms: 0 + -2 = -2 -3v = -2 Divide each side by '-3'. v = 0.6666666667 Simplifying v = 0.6666666667Solution
v = {0.4, 0.6666666667}
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