2v^2-114=7v

Solution for 2v^2-114=7v equation:

Simplifying
2v2 + -114 = 7v

Reorder the terms:
-114 + 2v2 = 7v

Solving
-114 + 2v2 = 7v

Solving for variable 'v'.

Reorder the terms:
-114 + -7v + 2v2 = 7v + -7v

Combine like terms: 7v + -7v = 0
-114 + -7v + 2v2 = 0

Factor a trinomial.
(-6 + -1v)(19 + -2v) = 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 '(19 + -2v)' equal to zero and attempt to solve:

Simplifying
19 + -2v = 0

Solving
19 + -2v = 0

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

Add '-19' to each side of the equation.
19 + -19 + -2v = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -2v = 0 + -19
-2v = 0 + -19

Combine like terms: 0 + -19 = -19
-2v = -19

Divide each side by '-2'.
v = 9.5

Simplifying
v = 9.5
Solution
v = {-6, 9.5}