7w=3w^2-6

Solution for 7w=3w^2-6 equation:

Simplifying
7w = 3w2 + -6

Reorder the terms:
7w = -6 + 3w2

Solving
7w = -6 + 3w2

Solving for variable 'w'.

Reorder the terms:
6 + 7w + -3w2 = -6 + 3w2 + 6 + -3w2

Reorder the terms:
6 + 7w + -3w2 = -6 + 6 + 3w2 + -3w2

Combine like terms: -6 + 6 = 0
6 + 7w + -3w2 = 0 + 3w2 + -3w2
6 + 7w + -3w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
6 + 7w + -3w2 = 0

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

Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Subproblem 2
Set the factor '(2 + 3w)' equal to zero and attempt to solve:

Simplifying
2 + 3w = 0

Solving
2 + 3w = 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 + 3w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3w = 0 + -2
3w = 0 + -2

Combine like terms: 0 + -2 = -2
3w = -2

Divide each side by '3'.
w = -0.6666666667

Simplifying
w = -0.6666666667
Solution
w = {3, -0.6666666667}