w^2+3w-9=2w+3

Solution for w^2+3w-9=2w+3 equation:

Simplifying
w2 + 3w + -9 = 2w + 3

Reorder the terms:
-9 + 3w + w2 = 2w + 3

Reorder the terms:
-9 + 3w + w2 = 3 + 2w

Solving
-9 + 3w + w2 = 3 + 2w

Solving for variable 'w'.

Reorder the terms:
-9 + -3 + 3w + -2w + w2 = 3 + 2w + -3 + -2w

Combine like terms: -9 + -3 = -12
-12 + 3w + -2w + w2 = 3 + 2w + -3 + -2w

Combine like terms: 3w + -2w = 1w
-12 + 1w + w2 = 3 + 2w + -3 + -2w

Reorder the terms:
-12 + 1w + w2 = 3 + -3 + 2w + -2w

Combine like terms: 3 + -3 = 0
-12 + 1w + w2 = 0 + 2w + -2w
-12 + 1w + w2 = 2w + -2w

Combine like terms: 2w + -2w = 0
-12 + 1w + w2 = 0

Factor a trinomial.
(-4 + -1w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve:

Simplifying
-4 + -1w = 0

Solving
-4 + -1w = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1w = 0 + 4
-1w = 0 + 4

Combine like terms: 0 + 4 = 4
-1w = 4

Divide each side by '-1'.
w = -4

Simplifying
w = -4
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 = {-4, 3}