2w^2-7w+27-w^2+10w-25=0

Solution for 2w^2-7w+27-w^2+10w-25=0 equation:

Simplifying
2w2 + -7w + 27 + -1w2 + 10w + -25 = 0

Reorder the terms:
27 + -25 + -7w + 10w + 2w2 + -1w2 = 0

Combine like terms: 27 + -25 = 2
2 + -7w + 10w + 2w2 + -1w2 = 0

Combine like terms: -7w + 10w = 3w
2 + 3w + 2w2 + -1w2 = 0

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

Solving
2 + 3w + 1w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(2 + w)(1 + w) = 0

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

Simplifying
1 + w = 0

Solving
1 + w = 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 + w = 0 + -1

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

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

Simplifying
w = -1
Solution
w = {-2, -1}