7w^2-13w=2

Solution for 7w^2-13w=2 equation:

Simplifying
7w2 + -13w = 2

Reorder the terms:
-13w + 7w2 = 2

Solving
-13w + 7w2 = 2

Solving for variable 'w'.

Reorder the terms:
-2 + -13w + 7w2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -13w + 7w2 = 0

Factor a trinomial.
(-1 + -7w)(2 + -1w) = 0

Subproblem 1
Set the factor '(-1 + -7w)' equal to zero and attempt to solve:

Simplifying
-1 + -7w = 0

Solving
-1 + -7w = 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 + -7w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7w = 0 + 1
-7w = 0 + 1

Combine like terms: 0 + 1 = 1
-7w = 1

Divide each side by '-7'.
w = -0.1428571429

Simplifying
w = -0.1428571429
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 = {-0.1428571429, 2}