(2w+2)(4w-1)=4w+1

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

Simplifying
(2w + 2)(4w + -1) = 4w + 1

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

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

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

Combine like terms: 8w + -2w = 6w
(-2 + 6w + 8w2) = 4w + 1

Reorder the terms:
-2 + 6w + 8w2 = 1 + 4w

Solving
-2 + 6w + 8w2 = 1 + 4w

Solving for variable 'w'.

Reorder the terms:
-2 + -1 + 6w + -4w + 8w2 = 1 + 4w + -1 + -4w

Combine like terms: -2 + -1 = -3
-3 + 6w + -4w + 8w2 = 1 + 4w + -1 + -4w

Combine like terms: 6w + -4w = 2w
-3 + 2w + 8w2 = 1 + 4w + -1 + -4w

Reorder the terms:
-3 + 2w + 8w2 = 1 + -1 + 4w + -4w

Combine like terms: 1 + -1 = 0
-3 + 2w + 8w2 = 0 + 4w + -4w
-3 + 2w + 8w2 = 4w + -4w

Combine like terms: 4w + -4w = 0
-3 + 2w + 8w2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
w = {-0.75, 0.5}