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Simplifying (4v + -6)(7 + v) = 0 Reorder the terms: (-6 + 4v)(7 + v) = 0 Multiply (-6 + 4v) * (7 + v) (-6(7 + v) + 4v * (7 + v)) = 0 ((7 * -6 + v * -6) + 4v * (7 + v)) = 0 ((-42 + -6v) + 4v * (7 + v)) = 0 (-42 + -6v + (7 * 4v + v * 4v)) = 0 (-42 + -6v + (28v + 4v2)) = 0 Combine like terms: -6v + 28v = 22v (-42 + 22v + 4v2) = 0 Solving -42 + 22v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 11v + 2v2) = 0 Factor a trinomial. 2((-7 + -1v)(3 + -2v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1v)' equal to zero and attempt to solve: Simplifying -7 + -1v = 0 Solving -7 + -1v = 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 + -1v = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1v = 0 + 7 -1v = 0 + 7 Combine like terms: 0 + 7 = 7 -1v = 7 Divide each side by '-1'. v = -7 Simplifying v = -7Subproblem 2
Set the factor '(3 + -2v)' equal to zero and attempt to solve: Simplifying 3 + -2v = 0 Solving 3 + -2v = 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 + -2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2v = 0 + -3 -2v = 0 + -3 Combine like terms: 0 + -3 = -3 -2v = -3 Divide each side by '-2'. v = 1.5 Simplifying v = 1.5Solution
v = {-7, 1.5}
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