4g+g^2=5

Solution for 4g+g^2=5 equation:

Simplifying
4g + g2 = 5

Solving
4g + g2 = 5

Solving for variable 'g'.

Reorder the terms:
-5 + 4g + g2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 4g + g2 = 0

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

Subproblem 1
Set the factor '(-5 + -1g)' equal to zero and attempt to solve:

Simplifying
-5 + -1g = 0

Solving
-5 + -1g = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1g = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1g = 0 + 5
-1g = 0 + 5

Combine like terms: 0 + 5 = 5
-1g = 5

Divide each side by '-1'.
g = -5

Simplifying
g = -5
Subproblem 2
Set the factor '(1 + -1g)' equal to zero and attempt to solve:

Simplifying
1 + -1g = 0

Solving
1 + -1g = 0

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

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

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

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

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

Simplifying
g = 1
Solution
g = {-5, 1}