w(2w-14)=60

Solution for w(2w-14)=60 equation:

Simplifying
w(2w + -14) = 60

Reorder the terms:
w(-14 + 2w) = 60
(-14 * w + 2w * w) = 60
(-14w + 2w2) = 60

Solving
-14w + 2w2 = 60

Solving for variable 'w'.

Reorder the terms:
-60 + -14w + 2w2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -14w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -7w + w2) = 0

Factor a trinomial.
2((-3 + -1w)(10 + -1w)) = 0

Ignore the factor 2.
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 '(10 + -1w)' equal to zero and attempt to solve:

Simplifying
10 + -1w = 0

Solving
10 + -1w = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1w = 0 + -10
-1w = 0 + -10

Combine like terms: 0 + -10 = -10
-1w = -10

Divide each side by '-1'.
w = 10

Simplifying
w = 10
Solution
w = {-3, 10}