w^2-6w+12=19

Solution for w^2-6w+12=19 equation:

Simplifying
w2 + -6w + 12 = 19

Reorder the terms:
12 + -6w + w2 = 19

Solving
12 + -6w + w2 = 19

Solving for variable 'w'.

Reorder the terms:
12 + -19 + -6w + w2 = 19 + -19

Combine like terms: 12 + -19 = -7
-7 + -6w + w2 = 19 + -19

Combine like terms: 19 + -19 = 0
-7 + -6w + w2 = 0

Factor a trinomial.
(-1 + -1w)(7 + -1w) = 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 '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1w = 0 + -7

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

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

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Solution
w = {-1, 7}