2w(4w+1)=12w+3

Solution for 2w(4w+1)=12w+3 equation:

Simplifying
2w(4w + 1) = 12w + 3

Reorder the terms:
2w(1 + 4w) = 12w + 3
(1 * 2w + 4w * 2w) = 12w + 3
(2w + 8w2) = 12w + 3

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

Solving
2w + 8w2 = 3 + 12w

Solving for variable 'w'.

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

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

Reorder the terms:
-3 + -10w + 8w2 = 3 + -3 + 12w + -12w

Combine like terms: 3 + -3 = 0
-3 + -10w + 8w2 = 0 + 12w + -12w
-3 + -10w + 8w2 = 12w + -12w

Combine like terms: 12w + -12w = 0
-3 + -10w + 8w2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
w = {-0.25, 1.5}