2w^2-7w=-6

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

Simplifying
2w2 + -7w = -6

Reorder the terms:
-7w + 2w2 = -6

Solving
-7w + 2w2 = -6

Solving for variable 'w'.

Reorder the terms:
6 + -7w + 2w2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + -7w + 2w2 = 0

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

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

Simplifying
2 + -1w = 0

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

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {1.5, 2}