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Simplifying (5v + 3)(2v + -7) = 0 Reorder the terms: (3 + 5v)(2v + -7) = 0 Reorder the terms: (3 + 5v)(-7 + 2v) = 0 Multiply (3 + 5v) * (-7 + 2v) (3(-7 + 2v) + 5v * (-7 + 2v)) = 0 ((-7 * 3 + 2v * 3) + 5v * (-7 + 2v)) = 0 ((-21 + 6v) + 5v * (-7 + 2v)) = 0 (-21 + 6v + (-7 * 5v + 2v * 5v)) = 0 (-21 + 6v + (-35v + 10v2)) = 0 Combine like terms: 6v + -35v = -29v (-21 + -29v + 10v2) = 0 Solving -21 + -29v + 10v2 = 0 Solving for variable 'v'. Factor a trinomial. (-3 + -5v)(7 + -2v) = 0Subproblem 1
Set the factor '(-3 + -5v)' equal to zero and attempt to solve: Simplifying -3 + -5v = 0 Solving -3 + -5v = 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 + -5v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5v = 0 + 3 -5v = 0 + 3 Combine like terms: 0 + 3 = 3 -5v = 3 Divide each side by '-5'. v = -0.6 Simplifying v = -0.6Subproblem 2
Set the factor '(7 + -2v)' equal to zero and attempt to solve: Simplifying 7 + -2v = 0 Solving 7 + -2v = 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 + -2v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2v = 0 + -7 -2v = 0 + -7 Combine like terms: 0 + -7 = -7 -2v = -7 Divide each side by '-2'. v = 3.5 Simplifying v = 3.5Solution
v = {-0.6, 3.5}
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