4g^2=4g-1

Solution for 4g^2=4g-1 equation:

Simplifying
4g2 = 4g + -1

Reorder the terms:
4g2 = -1 + 4g

Solving
4g2 = -1 + 4g

Solving for variable 'g'.

Reorder the terms:
1 + -4g + 4g2 = -1 + 4g + 1 + -4g

Reorder the terms:
1 + -4g + 4g2 = -1 + 1 + 4g + -4g

Combine like terms: -1 + 1 = 0
1 + -4g + 4g2 = 0 + 4g + -4g
1 + -4g + 4g2 = 4g + -4g

Combine like terms: 4g + -4g = 0
1 + -4g + 4g2 = 0

Factor a trinomial.
(1 + -2g)(1 + -2g) = 0

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

Simplifying
1 + -2g = 0

Solving
1 + -2g = 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 + -2g = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2g = 0 + -1
-2g = 0 + -1

Combine like terms: 0 + -1 = -1
-2g = -1

Divide each side by '-2'.
g = 0.5

Simplifying
g = 0.5
Subproblem 2
Set the factor '(1 + -2g)' equal to zero and attempt to solve:

Simplifying
1 + -2g = 0

Solving
1 + -2g = 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 + -2g = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2g = 0 + -1
-2g = 0 + -1

Combine like terms: 0 + -1 = -1
-2g = -1

Divide each side by '-2'.
g = 0.5

Simplifying
g = 0.5
Solution
g = {0.5, 0.5}