(v-1)(v-7)=0

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Solution for (v-1)(v-7)=0 equation: 


Simplifying
(v + -1)(v + -7) = 0

Reorder the terms:
(-1 + v)(v + -7) = 0

Reorder the terms:
(-1 + v)(-7 + v) = 0

Multiply (-1 + v) * (-7 + v)
(-1(-7 + v) + v(-7 + v)) = 0
((-7 * -1 + v * -1) + v(-7 + v)) = 0
((7 + -1v) + v(-7 + v)) = 0
(7 + -1v + (-7 * v + v * v)) = 0
(7 + -1v + (-7v + v2)) = 0

Combine like terms: -1v + -7v = -8v
(7 + -8v + v2) = 0

Solving
7 + -8v + v2 = 0

Solving for variable 'v'.

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


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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1v = 0 + -1

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

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

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

Simplifying
v = 1

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 = {1, 7}

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