3w^2+w=2(w+2)

Solution for 3w^2+w=2(w+2) equation:

Simplifying
3w2 + w = 2(w + 2)

Reorder the terms:
w + 3w2 = 2(w + 2)

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

Solving
w + 3w2 = 4 + 2w

Solving for variable 'w'.

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

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

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

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

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

Factor a trinomial.
(-1 + -1w)(4 + -3w) = 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 '(4 + -3w)' equal to zero and attempt to solve:

Simplifying
4 + -3w = 0

Solving
4 + -3w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3w = 0 + -4

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

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

Divide each side by '-3'.
w = 1.333333333

Simplifying
w = 1.333333333
Solution
w = {-1, 1.333333333}