(u*2-3u-18)(6u-12)=0

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Solution for (u*2-3u-18)(6u-12)=0 equation: 


Simplifying
(u * 2 + -3u + -18)(6u + -12) = 0

Reorder the terms for easier multiplication:
(2u + -3u + -18)(6u + -12) = 0

Reorder the terms:
(-18 + 2u + -3u)(6u + -12) = 0

Combine like terms: 2u + -3u = -1u
(-18 + -1u)(6u + -12) = 0

Reorder the terms:
(-18 + -1u)(-12 + 6u) = 0

Multiply (-18 + -1u) * (-12 + 6u)
(-18(-12 + 6u) + -1u * (-12 + 6u)) = 0
((-12 * -18 + 6u * -18) + -1u * (-12 + 6u)) = 0
((216 + -108u) + -1u * (-12 + 6u)) = 0
(216 + -108u + (-12 * -1u + 6u * -1u)) = 0
(216 + -108u + (12u + -6u2)) = 0

Combine like terms: -108u + 12u = -96u
(216 + -96u + -6u2) = 0

Solving
216 + -96u + -6u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '6'.
6(36 + -16u + -1u2) = 0

Factor a trinomial.
6((2 + -1u)(18 + u)) = 0

Ignore the factor 6.

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

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

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

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

Divide each side by '-1'.
u = 2

Simplifying
u = 2

Subproblem 2
Set the factor '(18 + u)' equal to zero and attempt to solve:

Simplifying
18 + u = 0

Solving
18 + u = 0

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

Add '-18' to each side of the equation.
18 + -18 + u = 0 + -18

Combine like terms: 18 + -18 = 0
0 + u = 0 + -18
u = 0 + -18

Combine like terms: 0 + -18 = -18
u = -18

Simplifying
u = -18
Solution
u = {2, -18}

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