234=2(w+3)(w-1)

Solution for 234=2(w+3)(w-1) equation:

Simplifying
234 = 2(w + 3)(w + -1)

Reorder the terms:
234 = 2(3 + w)(w + -1)

Reorder the terms:
234 = 2(3 + w)(-1 + w)

Multiply (3 + w) * (-1 + w)
234 = 2(3(-1 + w) + w(-1 + w))
234 = 2((-1 * 3 + w * 3) + w(-1 + w))
234 = 2((-3 + 3w) + w(-1 + w))
234 = 2(-3 + 3w + (-1 * w + w * w))
234 = 2(-3 + 3w + (-1w + w2))

Combine like terms: 3w + -1w = 2w
234 = 2(-3 + 2w + w2)
234 = (-3 * 2 + 2w * 2 + w2 * 2)
234 = (-6 + 4w + 2w2)

Solving
234 = -6 + 4w + 2w2

Solving for variable 'w'.

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

Reorder the terms:
240 + -4w + -2w2 = -6 + 6 + 4w + -4w + 2w2 + -2w2

Combine like terms: -6 + 6 = 0
240 + -4w + -2w2 = 0 + 4w + -4w + 2w2 + -2w2
240 + -4w + -2w2 = 4w + -4w + 2w2 + -2w2

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(120 + -2w + -1w2) = 0

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

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

Simplifying
12 + w = 0

Solving
12 + w = 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 + w = 0 + -12

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

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

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