4y(y+2)=4y+3

Solution for 4y(y+2)=4y+3 equation:

Simplifying
4y(y + 2) = 4y + 3

Reorder the terms:
4y(2 + y) = 4y + 3
(2 * 4y + y * 4y) = 4y + 3
(8y + 4y2) = 4y + 3

Reorder the terms:
8y + 4y2 = 3 + 4y

Solving
8y + 4y2 = 3 + 4y

Solving for variable 'y'.

Reorder the terms:
-3 + 8y + -4y + 4y2 = 3 + 4y + -3 + -4y

Combine like terms: 8y + -4y = 4y
-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.
(-3 + -2y)(1 + -2y) = 0

Subproblem 1
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
Subproblem 2
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
Solution
y = {-1.5, 0.5}