w^2+12=6w+3

Solution for w^2+12=6w+3 equation:

Simplifying
w2 + 12 = 6w + 3

Reorder the terms:
12 + w2 = 6w + 3

Reorder the terms:
12 + w2 = 3 + 6w

Solving
12 + w2 = 3 + 6w

Solving for variable 'w'.

Reorder the terms:
12 + -3 + -6w + w2 = 3 + 6w + -3 + -6w

Combine like terms: 12 + -3 = 9
9 + -6w + w2 = 3 + 6w + -3 + -6w

Reorder the terms:
9 + -6w + w2 = 3 + -3 + 6w + -6w

Combine like terms: 3 + -3 = 0
9 + -6w + w2 = 0 + 6w + -6w
9 + -6w + w2 = 6w + -6w

Combine like terms: 6w + -6w = 0
9 + -6w + w2 = 0

Factor a trinomial.
(3 + -1w)(3 + -1w) = 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 '(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
Solution
w = {3, 3}