(u-11)(u-6)+(2u-3)(u-12)=u(2u-40)+134

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Solution for (u-11)(u-6)+(2u-3)(u-12)=u(2u-40)+134 equation: 


Simplifying
(u + -11)(u + -6) + (2u + -3)(u + -12) = u(2u + -40) + 134

Reorder the terms:
(-11 + u)(u + -6) + (2u + -3)(u + -12) = u(2u + -40) + 134

Reorder the terms:
(-11 + u)(-6 + u) + (2u + -3)(u + -12) = u(2u + -40) + 134

Multiply (-11 + u) * (-6 + u)
(-11(-6 + u) + u(-6 + u)) + (2u + -3)(u + -12) = u(2u + -40) + 134
((-6 * -11 + u * -11) + u(-6 + u)) + (2u + -3)(u + -12) = u(2u + -40) + 134
((66 + -11u) + u(-6 + u)) + (2u + -3)(u + -12) = u(2u + -40) + 134
(66 + -11u + (-6 * u + u * u)) + (2u + -3)(u + -12) = u(2u + -40) + 134
(66 + -11u + (-6u + u2)) + (2u + -3)(u + -12) = u(2u + -40) + 134

Combine like terms: -11u + -6u = -17u
(66 + -17u + u2) + (2u + -3)(u + -12) = u(2u + -40) + 134

Reorder the terms:
66 + -17u + u2 + (-3 + 2u)(u + -12) = u(2u + -40) + 134

Reorder the terms:
66 + -17u + u2 + (-3 + 2u)(-12 + u) = u(2u + -40) + 134

Multiply (-3 + 2u) * (-12 + u)
66 + -17u + u2 + (-3(-12 + u) + 2u * (-12 + u)) = u(2u + -40) + 134
66 + -17u + u2 + ((-12 * -3 + u * -3) + 2u * (-12 + u)) = u(2u + -40) + 134
66 + -17u + u2 + ((36 + -3u) + 2u * (-12 + u)) = u(2u + -40) + 134
66 + -17u + u2 + (36 + -3u + (-12 * 2u + u * 2u)) = u(2u + -40) + 134
66 + -17u + u2 + (36 + -3u + (-24u + 2u2)) = u(2u + -40) + 134

Combine like terms: -3u + -24u = -27u
66 + -17u + u2 + (36 + -27u + 2u2) = u(2u + -40) + 134

Reorder the terms:
66 + 36 + -17u + -27u + u2 + 2u2 = u(2u + -40) + 134

Combine like terms: 66 + 36 = 102
102 + -17u + -27u + u2 + 2u2 = u(2u + -40) + 134

Combine like terms: -17u + -27u = -44u
102 + -44u + u2 + 2u2 = u(2u + -40) + 134

Combine like terms: u2 + 2u2 = 3u2
102 + -44u + 3u2 = u(2u + -40) + 134

Reorder the terms:
102 + -44u + 3u2 = u(-40 + 2u) + 134
102 + -44u + 3u2 = (-40 * u + 2u * u) + 134
102 + -44u + 3u2 = (-40u + 2u2) + 134

Reorder the terms:
102 + -44u + 3u2 = 134 + -40u + 2u2

Solving
102 + -44u + 3u2 = 134 + -40u + 2u2

Solving for variable 'u'.

Reorder the terms:
102 + -134 + -44u + 40u + 3u2 + -2u2 = 134 + -40u + 2u2 + -134 + 40u + -2u2

Combine like terms: 102 + -134 = -32
-32 + -44u + 40u + 3u2 + -2u2 = 134 + -40u + 2u2 + -134 + 40u + -2u2

Combine like terms: -44u + 40u = -4u
-32 + -4u + 3u2 + -2u2 = 134 + -40u + 2u2 + -134 + 40u + -2u2

Combine like terms: 3u2 + -2u2 = 1u2
-32 + -4u + 1u2 = 134 + -40u + 2u2 + -134 + 40u + -2u2

Reorder the terms:
-32 + -4u + 1u2 = 134 + -134 + -40u + 40u + 2u2 + -2u2

Combine like terms: 134 + -134 = 0
-32 + -4u + 1u2 = 0 + -40u + 40u + 2u2 + -2u2
-32 + -4u + 1u2 = -40u + 40u + 2u2 + -2u2

Combine like terms: -40u + 40u = 0
-32 + -4u + 1u2 = 0 + 2u2 + -2u2
-32 + -4u + 1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-32 + -4u + 1u2 = 0

Factor a trinomial.
(-4 + -1u)(8 + -1u) = 0


Subproblem 1
Set the factor '(-4 + -1u)' equal to zero and attempt to solve:

Simplifying
-4 + -1u = 0

Solving
-4 + -1u = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1u = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1u = 0 + 4
-1u = 0 + 4

Combine like terms: 0 + 4 = 4
-1u = 4

Divide each side by '-1'.
u = -4

Simplifying
u = -4

Subproblem 2
Set the factor '(8 + -1u)' equal to zero and attempt to solve:

Simplifying
8 + -1u = 0

Solving
8 + -1u = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1u = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1u = 0 + -8
-1u = 0 + -8

Combine like terms: 0 + -8 = -8
-1u = -8

Divide each side by '-1'.
u = 8

Simplifying
u = 8
Solution
u = {-4, 8}

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