0=w^2-7w+6

Solution for 0=w^2-7w+6 equation:

Simplifying
0 = w2 + -7w + 6

Reorder the terms:
0 = 6 + -7w + w2

Solving
0 = 6 + -7w + w2

Solving for variable 'w'.

Combine like terms: 0 + -6 = -6
-6 + 7w + -1w2 = 6 + -7w + w2 + -6 + 7w + -1w2

Reorder the terms:
-6 + 7w + -1w2 = 6 + -6 + -7w + 7w + w2 + -1w2

Combine like terms: 6 + -6 = 0
-6 + 7w + -1w2 = 0 + -7w + 7w + w2 + -1w2
-6 + 7w + -1w2 = -7w + 7w + w2 + -1w2

Combine like terms: -7w + 7w = 0
-6 + 7w + -1w2 = 0 + w2 + -1w2
-6 + 7w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
-6 + 7w + -1w2 = 0

Factor a trinomial.
(-6 + w)(1 + -1w) = 0

Subproblem 1
Set the factor '(-6 + w)' equal to zero and attempt to solve:

Simplifying
-6 + w = 0

Solving
-6 + w = 0

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

Add '6' to each side of the equation.
-6 + 6 + w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + w = 0 + 6
w = 0 + 6

Combine like terms: 0 + 6 = 6
w = 6

Simplifying
w = 6
Subproblem 2
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
Solution
w = {6, 1}