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Simplifying (5v + -1)(6v + -3) = 0 Reorder the terms: (-1 + 5v)(6v + -3) = 0 Reorder the terms: (-1 + 5v)(-3 + 6v) = 0 Multiply (-1 + 5v) * (-3 + 6v) (-1(-3 + 6v) + 5v * (-3 + 6v)) = 0 ((-3 * -1 + 6v * -1) + 5v * (-3 + 6v)) = 0 ((3 + -6v) + 5v * (-3 + 6v)) = 0 (3 + -6v + (-3 * 5v + 6v * 5v)) = 0 (3 + -6v + (-15v + 30v2)) = 0 Combine like terms: -6v + -15v = -21v (3 + -21v + 30v2) = 0 Solving 3 + -21v + 30v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -7v + 10v2) = 0 Factor a trinomial. 3((1 + -5v)(1 + -2v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -5v)' equal to zero and attempt to solve: Simplifying 1 + -5v = 0 Solving 1 + -5v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5v = 0 + -1 -5v = 0 + -1 Combine like terms: 0 + -1 = -1 -5v = -1 Divide each side by '-5'. v = 0.2 Simplifying v = 0.2Subproblem 2
Set the factor '(1 + -2v)' equal to zero and attempt to solve: Simplifying 1 + -2v = 0 Solving 1 + -2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2v = 0 + -1 -2v = 0 + -1 Combine like terms: 0 + -1 = -1 -2v = -1 Divide each side by '-2'. v = 0.5 Simplifying v = 0.5Solution
v = {0.2, 0.5}
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