w(4w+6)+2w=2(2w+7w-3)

Solution for w(4w+6)+2w=2(2w+7w-3) equation:

Simplifying
w(4w + 6) + 2w = 2(2w + 7w + -3)

Reorder the terms:
w(6 + 4w) + 2w = 2(2w + 7w + -3)
(6 * w + 4w * w) + 2w = 2(2w + 7w + -3)
(6w + 4w2) + 2w = 2(2w + 7w + -3)

Reorder the terms:
6w + 2w + 4w2 = 2(2w + 7w + -3)

Combine like terms: 6w + 2w = 8w
8w + 4w2 = 2(2w + 7w + -3)

Reorder the terms:
8w + 4w2 = 2(-3 + 2w + 7w)

Combine like terms: 2w + 7w = 9w
8w + 4w2 = 2(-3 + 9w)
8w + 4w2 = (-3 * 2 + 9w * 2)
8w + 4w2 = (-6 + 18w)

Solving
8w + 4w2 = -6 + 18w

Solving for variable 'w'.

Reorder the terms:
6 + 8w + -18w + 4w2 = -6 + 18w + 6 + -18w

Combine like terms: 8w + -18w = -10w
6 + -10w + 4w2 = -6 + 18w + 6 + -18w

Reorder the terms:
6 + -10w + 4w2 = -6 + 6 + 18w + -18w

Combine like terms: -6 + 6 = 0
6 + -10w + 4w2 = 0 + 18w + -18w
6 + -10w + 4w2 = 18w + -18w

Combine like terms: 18w + -18w = 0
6 + -10w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -5w + 2w2) = 0

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

Ignore the factor 2.
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 + -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 = {1, 1.5}