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Simplifying (1 + v)(4v + -7) = 0 Reorder the terms: (1 + v)(-7 + 4v) = 0 Multiply (1 + v) * (-7 + 4v) (1(-7 + 4v) + v(-7 + 4v)) = 0 ((-7 * 1 + 4v * 1) + v(-7 + 4v)) = 0 ((-7 + 4v) + v(-7 + 4v)) = 0 (-7 + 4v + (-7 * v + 4v * v)) = 0 (-7 + 4v + (-7v + 4v2)) = 0 Combine like terms: 4v + -7v = -3v (-7 + -3v + 4v2) = 0 Solving -7 + -3v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-1 + -1v)(7 + -4v) = 0Subproblem 1
Set the factor '(-1 + -1v)' equal to zero and attempt to solve: Simplifying -1 + -1v = 0 Solving -1 + -1v = 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 + -1v = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1v = 0 + 1 -1v = 0 + 1 Combine like terms: 0 + 1 = 1 -1v = 1 Divide each side by '-1'. v = -1 Simplifying v = -1Subproblem 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 = {-1, 1.75}
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