576v^2+1=-48v

Solution for 576v^2+1=-48v equation:

Simplifying
576v2 + 1 = -48v

Reorder the terms:
1 + 576v2 = -48v

Solving
1 + 576v2 = -48v

Solving for variable 'v'.

Reorder the terms:
1 + 48v + 576v2 = -48v + 48v

Combine like terms: -48v + 48v = 0
1 + 48v + 576v2 = 0

Factor a trinomial.
(1 + 24v)(1 + 24v) = 0

Subproblem 1
Set the factor '(1 + 24v)' equal to zero and attempt to solve:

Simplifying
1 + 24v = 0

Solving
1 + 24v = 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 + 24v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 24v = 0 + -1
24v = 0 + -1

Combine like terms: 0 + -1 = -1
24v = -1

Divide each side by '24'.
v = -0.04166666667

Simplifying
v = -0.04166666667
Subproblem 2
Set the factor '(1 + 24v)' equal to zero and attempt to solve:

Simplifying
1 + 24v = 0

Solving
1 + 24v = 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 + 24v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 24v = 0 + -1
24v = 0 + -1

Combine like terms: 0 + -1 = -1
24v = -1

Divide each side by '24'.
v = -0.04166666667

Simplifying
v = -0.04166666667
Solution
v = {-0.04166666667, -0.04166666667}