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Simplifying (5 + -1v)(3v + 8) = 0 Reorder the terms: (5 + -1v)(8 + 3v) = 0 Multiply (5 + -1v) * (8 + 3v) (5(8 + 3v) + -1v * (8 + 3v)) = 0 ((8 * 5 + 3v * 5) + -1v * (8 + 3v)) = 0 ((40 + 15v) + -1v * (8 + 3v)) = 0 (40 + 15v + (8 * -1v + 3v * -1v)) = 0 (40 + 15v + (-8v + -3v2)) = 0 Combine like terms: 15v + -8v = 7v (40 + 7v + -3v2) = 0 Solving 40 + 7v + -3v2 = 0 Solving for variable 'v'. Factor a trinomial. (5 + -1v)(8 + 3v) = 0Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 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 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Subproblem 2
Set the factor '(8 + 3v)' equal to zero and attempt to solve: Simplifying 8 + 3v = 0 Solving 8 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3v = 0 + -8 3v = 0 + -8 Combine like terms: 0 + -8 = -8 3v = -8 Divide each side by '3'. v = -2.666666667 Simplifying v = -2.666666667Solution
v = {5, -2.666666667}
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