(w-1)(2w+6)=234

Solution for (w-1)(2w+6)=234 equation:

Simplifying
(w + -1)(2w + 6) = 234

Reorder the terms:
(-1 + w)(2w + 6) = 234

Reorder the terms:
(-1 + w)(6 + 2w) = 234

Multiply (-1 + w) * (6 + 2w)
(-1(6 + 2w) + w(6 + 2w)) = 234
((6 * -1 + 2w * -1) + w(6 + 2w)) = 234
((-6 + -2w) + w(6 + 2w)) = 234
(-6 + -2w + (6 * w + 2w * w)) = 234
(-6 + -2w + (6w + 2w2)) = 234

Combine like terms: -2w + 6w = 4w
(-6 + 4w + 2w2) = 234

Solving
-6 + 4w + 2w2 = 234

Solving for variable 'w'.

Reorder the terms:
-6 + -234 + 4w + 2w2 = 234 + -234

Combine like terms: -6 + -234 = -240
-240 + 4w + 2w2 = 234 + -234

Combine like terms: 234 + -234 = 0
-240 + 4w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-120 + 2w + w2) = 0

Factor a trinomial.
2((-12 + -1w)(10 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -1w)' equal to zero and attempt to solve:

Simplifying
-12 + -1w = 0

Solving
-12 + -1w = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1w = 0 + 12

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

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

Divide each side by '-1'.
w = -12

Simplifying
w = -12
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 = {-12, 10}