(7v+5)(2v-7)=0

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Solution for (7v+5)(2v-7)=0 equation:


Simplifying
(7v + 5)(2v + -7) = 0

Reorder the terms:
(5 + 7v)(2v + -7) = 0

Reorder the terms:
(5 + 7v)(-7 + 2v) = 0

Multiply (5 + 7v) * (-7 + 2v)
(5(-7 + 2v) + 7v * (-7 + 2v)) = 0
((-7 * 5 + 2v * 5) + 7v * (-7 + 2v)) = 0
((-35 + 10v) + 7v * (-7 + 2v)) = 0
(-35 + 10v + (-7 * 7v + 2v * 7v)) = 0
(-35 + 10v + (-49v + 14v2)) = 0

Combine like terms: 10v + -49v = -39v
(-35 + -39v + 14v2) = 0

Solving
-35 + -39v + 14v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-5 + -7v)(7 + -2v) = 0

Subproblem 1

Set the factor '(-5 + -7v)' equal to zero and attempt to solve: Simplifying -5 + -7v = 0 Solving -5 + -7v = 0 Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -7v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7v = 0 + 5 -7v = 0 + 5 Combine like terms: 0 + 5 = 5 -7v = 5 Divide each side by '-7'. v = -0.7142857143 Simplifying v = -0.7142857143

Subproblem 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 = 3.5

Solution

v = {-0.7142857143, 3.5}

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