2w^2+15w+23=w+3

Solution for 2w^2+15w+23=w+3 equation:

Simplifying
2w2 + 15w + 23 = w + 3

Reorder the terms:
23 + 15w + 2w2 = w + 3

Reorder the terms:
23 + 15w + 2w2 = 3 + w

Solving
23 + 15w + 2w2 = 3 + w

Solving for variable 'w'.

Reorder the terms:
23 + -3 + 15w + -1w + 2w2 = 3 + w + -3 + -1w

Combine like terms: 23 + -3 = 20
20 + 15w + -1w + 2w2 = 3 + w + -3 + -1w

Combine like terms: 15w + -1w = 14w
20 + 14w + 2w2 = 3 + w + -3 + -1w

Reorder the terms:
20 + 14w + 2w2 = 3 + -3 + w + -1w

Combine like terms: 3 + -3 = 0
20 + 14w + 2w2 = 0 + w + -1w
20 + 14w + 2w2 = w + -1w

Combine like terms: w + -1w = 0
20 + 14w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 7w + w2) = 0

Factor a trinomial.
2((5 + w)(2 + w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

Simplifying
w = -2
Solution
w = {-5, -2}