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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 = 15v (-14 + 15v + -4v2) = 0 Solving -14 + 15v + -4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-2 + v)(7 + -4v) = 0Subproblem 1
Set the factor '(-2 + v)' equal to zero and attempt to solve: Simplifying -2 + v = 0 Solving -2 + v = 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 + v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + v = 0 + 2 v = 0 + 2 Combine like terms: 0 + 2 = 2 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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