(4w+1)w=3

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

Simplifying
(4w + 1) * w = 3

Reorder the terms:
(1 + 4w) * w = 3

Reorder the terms for easier multiplication:
w(1 + 4w) = 3
(1 * w + 4w * w) = 3
(1w + 4w2) = 3

Solving
1w + 4w2 = 3

Solving for variable 'w'.

Reorder the terms:
-3 + 1w + 4w2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 1w + 4w2 = 0

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

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 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 + -1w = 0 + 1

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

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

Divide each side by '-1'.
w = -1

Simplifying
w = -1
Subproblem 2
Set the factor '(3 + -4w)' equal to zero and attempt to solve:

Simplifying
3 + -4w = 0

Solving
3 + -4w = 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 + -4w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4w = 0 + -3
-4w = 0 + -3

Combine like terms: 0 + -3 = -3
-4w = -3

Divide each side by '-4'.
w = 0.75

Simplifying
w = 0.75
Solution
w = {-1, 0.75}