(9w^2-30w+25)-(w^2+14w+49)=0

Solution for (9w^2-30w+25)-(w^2+14w+49)=0 equation:

Simplifying
(9w2 + -30w + 25) + -1(w2 + 14w + 49) = 0

Reorder the terms:
(25 + -30w + 9w2) + -1(w2 + 14w + 49) = 0

Remove parenthesis around (25 + -30w + 9w2)
25 + -30w + 9w2 + -1(w2 + 14w + 49) = 0

Reorder the terms:
25 + -30w + 9w2 + -1(49 + 14w + w2) = 0
25 + -30w + 9w2 + (49 * -1 + 14w * -1 + w2 * -1) = 0
25 + -30w + 9w2 + (-49 + -14w + -1w2) = 0

Reorder the terms:
25 + -49 + -30w + -14w + 9w2 + -1w2 = 0

Combine like terms: 25 + -49 = -24
-24 + -30w + -14w + 9w2 + -1w2 = 0

Combine like terms: -30w + -14w = -44w
-24 + -44w + 9w2 + -1w2 = 0

Combine like terms: 9w2 + -1w2 = 8w2
-24 + -44w + 8w2 = 0

Solving
-24 + -44w + 8w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -11w + 2w2) = 0

Factor a trinomial.
4((-1 + -2w)(6 + -1w)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -2w)' equal to zero and attempt to solve:

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 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 + -2w = 0 + 1

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

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

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {-0.5, 6}