4w(2w+3)=2w+3

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

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

Reorder the terms:
4w(3 + 2w) = 2w + 3
(3 * 4w + 2w * 4w) = 2w + 3
(12w + 8w2) = 2w + 3

Reorder the terms:
12w + 8w2 = 3 + 2w

Solving
12w + 8w2 = 3 + 2w

Solving for variable 'w'.

Reorder the terms:
-3 + 12w + -2w + 8w2 = 3 + 2w + -3 + -2w

Combine like terms: 12w + -2w = 10w
-3 + 10w + 8w2 = 3 + 2w + -3 + -2w

Reorder the terms:
-3 + 10w + 8w2 = 3 + -3 + 2w + -2w

Combine like terms: 3 + -3 = 0
-3 + 10w + 8w2 = 0 + 2w + -2w
-3 + 10w + 8w2 = 2w + -2w

Combine like terms: 2w + -2w = 0
-3 + 10w + 8w2 = 0

Factor a trinomial.
(-3 + -2w)(1 + -4w) = 0

Subproblem 1
Set the factor '(-3 + -2w)' equal to zero and attempt to solve:

Simplifying
-3 + -2w = 0

Solving
-3 + -2w = 0

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

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

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

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

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

Simplifying
w = -1.5
Subproblem 2
Set the factor '(1 + -4w)' equal to zero and attempt to solve:

Simplifying
1 + -4w = 0

Solving
1 + -4w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4w = 0 + -1
-4w = 0 + -1

Combine like terms: 0 + -1 = -1
-4w = -1

Divide each side by '-4'.
w = 0.25

Simplifying
w = 0.25
Solution
w = {-1.5, 0.25}