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Simplifying (2 + -1v)(4v + 7) = 0 Reorder the terms: (2 + -1v)(7 + 4v) = 0 Multiply (2 + -1v) * (7 + 4v) (2(7 + 4v) + -1v * (7 + 4v)) = 0 ((7 * 2 + 4v * 2) + -1v * (7 + 4v)) = 0 ((14 + 8v) + -1v * (7 + 4v)) = 0 (14 + 8v + (7 * -1v + 4v * -1v)) = 0 (14 + 8v + (-7v + -4v2)) = 0 Combine like terms: 8v + -7v = 1v (14 + 1v + -4v2) = 0 Solving 14 + 1v + -4v2 = 0 Solving for variable 'v'. Factor a trinomial. (2 + -1v)(7 + 4v) = 0Subproblem 1
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 = 2Subproblem 2
Set the factor '(7 + 4v)' equal to zero and attempt to solve: Simplifying 7 + 4v = 0 Solving 7 + 4v = 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 + 4v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4v = 0 + -7 4v = 0 + -7 Combine like terms: 0 + -7 = -7 4v = -7 Divide each side by '4'. v = -1.75 Simplifying v = -1.75Solution
v = {2, -1.75}
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