49v^2-5=28v

Solution for 49v^2-5=28v equation:

Simplifying
49v2 + -5 = 28v

Reorder the terms:
-5 + 49v2 = 28v

Solving
-5 + 49v2 = 28v

Solving for variable 'v'.

Reorder the terms:
-5 + -28v + 49v2 = 28v + -28v

Combine like terms: 28v + -28v = 0
-5 + -28v + 49v2 = 0

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

Subproblem 1
Set the factor '(-1 + -7v)' equal to zero and attempt to solve:

Simplifying
-1 + -7v = 0

Solving
-1 + -7v = 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 + -7v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7v = 0 + 1
-7v = 0 + 1

Combine like terms: 0 + 1 = 1
-7v = 1

Divide each side by '-7'.
v = -0.1428571429

Simplifying
v = -0.1428571429
Subproblem 2
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
Solution
v = {-0.1428571429, 0.7142857143}