4y^2=3+4y

Solution for 4y^2=3+4y equation:

Simplifying
4y2 = 3 + 4y

Solving
4y2 = 3 + 4y

Solving for variable 'y'.

Reorder the terms:
-3 + -4y + 4y2 = 3 + 4y + -3 + -4y

Reorder the terms:
-3 + -4y + 4y2 = 3 + -3 + 4y + -4y

Combine like terms: 3 + -3 = 0
-3 + -4y + 4y2 = 0 + 4y + -4y
-3 + -4y + 4y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-3 + -4y + 4y2 = 0

Factor a trinomial.
(-1 + -2y)(3 + -2y) = 0

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

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2y = 0 + 1

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

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

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

Simplifying
y = -0.5
Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-0.5, 1.5}