(5w+2)(2w+1)=8w+4

Solution for (5w+2)(2w+1)=8w+4 equation:

Simplifying
(5w + 2)(2w + 1) = 8w + 4

Reorder the terms:
(2 + 5w)(2w + 1) = 8w + 4

Reorder the terms:
(2 + 5w)(1 + 2w) = 8w + 4

Multiply (2 + 5w) * (1 + 2w)
(2(1 + 2w) + 5w * (1 + 2w)) = 8w + 4
((1 * 2 + 2w * 2) + 5w * (1 + 2w)) = 8w + 4
((2 + 4w) + 5w * (1 + 2w)) = 8w + 4
(2 + 4w + (1 * 5w + 2w * 5w)) = 8w + 4
(2 + 4w + (5w + 10w2)) = 8w + 4

Combine like terms: 4w + 5w = 9w
(2 + 9w + 10w2) = 8w + 4

Reorder the terms:
2 + 9w + 10w2 = 4 + 8w

Solving
2 + 9w + 10w2 = 4 + 8w

Solving for variable 'w'.

Reorder the terms:
2 + -4 + 9w + -8w + 10w2 = 4 + 8w + -4 + -8w

Combine like terms: 2 + -4 = -2
-2 + 9w + -8w + 10w2 = 4 + 8w + -4 + -8w

Combine like terms: 9w + -8w = 1w
-2 + 1w + 10w2 = 4 + 8w + -4 + -8w

Reorder the terms:
-2 + 1w + 10w2 = 4 + -4 + 8w + -8w

Combine like terms: 4 + -4 = 0
-2 + 1w + 10w2 = 0 + 8w + -8w
-2 + 1w + 10w2 = 8w + -8w

Combine like terms: 8w + -8w = 0
-2 + 1w + 10w2 = 0

Factor a trinomial.
(-1 + -2w)(2 + -5w) = 0

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

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 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 + -2w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2w = 0 + 1
-2w = 0 + 1

Combine like terms: 0 + 1 = 1
-2w = 1

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 2
Set the factor '(2 + -5w)' equal to zero and attempt to solve:

Simplifying
2 + -5w = 0

Solving
2 + -5w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5w = 0 + -2
-5w = 0 + -2

Combine like terms: 0 + -2 = -2
-5w = -2

Divide each side by '-5'.
w = 0.4

Simplifying
w = 0.4
Solution
w = {-0.5, 0.4}