5w(4w+1)=4w+1

Solution for 5w(4w+1)=4w+1 equation:

Simplifying
5w(4w + 1) = 4w + 1

Reorder the terms:
5w(1 + 4w) = 4w + 1
(1 * 5w + 4w * 5w) = 4w + 1
(5w + 20w2) = 4w + 1

Reorder the terms:
5w + 20w2 = 1 + 4w

Solving
5w + 20w2 = 1 + 4w

Solving for variable 'w'.

Reorder the terms:
-1 + 5w + -4w + 20w2 = 1 + 4w + -1 + -4w

Combine like terms: 5w + -4w = 1w
-1 + 1w + 20w2 = 1 + 4w + -1 + -4w

Reorder the terms:
-1 + 1w + 20w2 = 1 + -1 + 4w + -4w

Combine like terms: 1 + -1 = 0
-1 + 1w + 20w2 = 0 + 4w + -4w
-1 + 1w + 20w2 = 4w + -4w

Combine like terms: 4w + -4w = 0
-1 + 1w + 20w2 = 0

Factor a trinomial.
(-1 + -4w)(1 + -5w) = 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 '(1 + -5w)' equal to zero and attempt to solve:

Simplifying
1 + -5w = 0

Solving
1 + -5w = 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 + -5w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5w = 0 + -1
-5w = 0 + -1

Combine like terms: 0 + -1 = -1
-5w = -1

Divide each side by '-5'.
w = 0.2

Simplifying
w = 0.2
Solution
w = {-0.25, 0.2}