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Simplifying (7v + -2)(5v + -7) = 0 Reorder the terms: (-2 + 7v)(5v + -7) = 0 Reorder the terms: (-2 + 7v)(-7 + 5v) = 0 Multiply (-2 + 7v) * (-7 + 5v) (-2(-7 + 5v) + 7v * (-7 + 5v)) = 0 ((-7 * -2 + 5v * -2) + 7v * (-7 + 5v)) = 0 ((14 + -10v) + 7v * (-7 + 5v)) = 0 (14 + -10v + (-7 * 7v + 5v * 7v)) = 0 (14 + -10v + (-49v + 35v2)) = 0 Combine like terms: -10v + -49v = -59v (14 + -59v + 35v2) = 0 Solving 14 + -59v + 35v2 = 0 Solving for variable 'v'. Factor a trinomial. (2 + -7v)(7 + -5v) = 0Subproblem 1
Set the factor '(2 + -7v)' equal to zero and attempt to solve: Simplifying 2 + -7v = 0 Solving 2 + -7v = 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 + -7v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7v = 0 + -2 -7v = 0 + -2 Combine like terms: 0 + -2 = -2 -7v = -2 Divide each side by '-7'. v = 0.2857142857 Simplifying v = 0.2857142857Subproblem 2
Set the factor '(7 + -5v)' equal to zero and attempt to solve: Simplifying 7 + -5v = 0 Solving 7 + -5v = 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 + -5v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5v = 0 + -7 -5v = 0 + -7 Combine like terms: 0 + -7 = -7 -5v = -7 Divide each side by '-5'. v = 1.4 Simplifying v = 1.4Solution
v = {0.2857142857, 1.4}
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