2u^2-5u-12=u^2-8u+16

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Solution for 2u^2-5u-12=u^2-8u+16 equation: 


Simplifying
2u2 + -5u + -12 = u2 + -8u + 16

Reorder the terms:
-12 + -5u + 2u2 = u2 + -8u + 16

Reorder the terms:
-12 + -5u + 2u2 = 16 + -8u + u2

Solving
-12 + -5u + 2u2 = 16 + -8u + u2

Solving for variable 'u'.

Reorder the terms:
-12 + -16 + -5u + 8u + 2u2 + -1u2 = 16 + -8u + u2 + -16 + 8u + -1u2

Combine like terms: -12 + -16 = -28
-28 + -5u + 8u + 2u2 + -1u2 = 16 + -8u + u2 + -16 + 8u + -1u2

Combine like terms: -5u + 8u = 3u
-28 + 3u + 2u2 + -1u2 = 16 + -8u + u2 + -16 + 8u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-28 + 3u + 1u2 = 16 + -8u + u2 + -16 + 8u + -1u2

Reorder the terms:
-28 + 3u + 1u2 = 16 + -16 + -8u + 8u + u2 + -1u2

Combine like terms: 16 + -16 = 0
-28 + 3u + 1u2 = 0 + -8u + 8u + u2 + -1u2
-28 + 3u + 1u2 = -8u + 8u + u2 + -1u2

Combine like terms: -8u + 8u = 0
-28 + 3u + 1u2 = 0 + u2 + -1u2
-28 + 3u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-28 + 3u + 1u2 = 0

Factor a trinomial.
(-7 + -1u)(4 + -1u) = 0


Subproblem 1
Set the factor '(-7 + -1u)' equal to zero and attempt to solve:

Simplifying
-7 + -1u = 0

Solving
-7 + -1u = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1u = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1u = 0 + 7
-1u = 0 + 7

Combine like terms: 0 + 7 = 7
-1u = 7

Divide each side by '-1'.
u = -7

Simplifying
u = -7

Subproblem 2
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
Solution
u = {-7, 4}

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