v^2-8v+16=2v^2-13v+10

Solution for v^2-8v+16=2v^2-13v+10 equation:

Simplifying
v2 + -8v + 16 = 2v2 + -13v + 10

Reorder the terms:
16 + -8v + v2 = 2v2 + -13v + 10

Reorder the terms:
16 + -8v + v2 = 10 + -13v + 2v2

Solving
16 + -8v + v2 = 10 + -13v + 2v2

Solving for variable 'v'.

Reorder the terms:
16 + -10 + -8v + 13v + v2 + -2v2 = 10 + -13v + 2v2 + -10 + 13v + -2v2

Combine like terms: 16 + -10 = 6
6 + -8v + 13v + v2 + -2v2 = 10 + -13v + 2v2 + -10 + 13v + -2v2

Combine like terms: -8v + 13v = 5v
6 + 5v + v2 + -2v2 = 10 + -13v + 2v2 + -10 + 13v + -2v2

Combine like terms: v2 + -2v2 = -1v2
6 + 5v + -1v2 = 10 + -13v + 2v2 + -10 + 13v + -2v2

Reorder the terms:
6 + 5v + -1v2 = 10 + -10 + -13v + 13v + 2v2 + -2v2

Combine like terms: 10 + -10 = 0
6 + 5v + -1v2 = 0 + -13v + 13v + 2v2 + -2v2
6 + 5v + -1v2 = -13v + 13v + 2v2 + -2v2

Combine like terms: -13v + 13v = 0
6 + 5v + -1v2 = 0 + 2v2 + -2v2
6 + 5v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
6 + 5v + -1v2 = 0

Factor a trinomial.
(6 + -1v)(1 + v) = 0

Subproblem 1
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

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

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

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

Simplifying
v = -1
Solution
v = {6, -1}