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

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


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

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

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

Multiply (-7 + v) * (-5 + v)
(-7(-5 + v) + v(-5 + v)) = 0
((-5 * -7 + v * -7) + v(-5 + v)) = 0
((35 + -7v) + v(-5 + v)) = 0
(35 + -7v + (-5 * v + v * v)) = 0
(35 + -7v + (-5v + v2)) = 0

Combine like terms: -7v + -5v = -12v
(35 + -12v + v2) = 0

Solving
35 + -12v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(5 + -1v)(7 + -1v) = 0


Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 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 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5

Subproblem 2
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 = 7
Solution
v = {5, 7}

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