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Simplifying (3 + v)(4v + -7) = 0 Reorder the terms: (3 + v)(-7 + 4v) = 0 Multiply (3 + v) * (-7 + 4v) (3(-7 + 4v) + v(-7 + 4v)) = 0 ((-7 * 3 + 4v * 3) + v(-7 + 4v)) = 0 ((-21 + 12v) + v(-7 + 4v)) = 0 (-21 + 12v + (-7 * v + 4v * v)) = 0 (-21 + 12v + (-7v + 4v2)) = 0 Combine like terms: 12v + -7v = 5v (-21 + 5v + 4v2) = 0 Solving -21 + 5v + 4v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -1v)(7 + -4v) = 0Subproblem 1
Set the factor '(-3 + -1v)' equal to zero and attempt to solve: Simplifying -3 + -1v = 0 Solving -3 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1v = 0 + 3 -1v = 0 + 3 Combine like terms: 0 + 3 = 3 -1v = 3 Divide each side by '-1'. v = -3 Simplifying v = -3Subproblem 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 = {-3, 1.75}
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