2u^2-8=u^2-3u+2

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Solution for 2u^2-8=u^2-3u+2 equation: 


Simplifying
2u2 + -8 = u2 + -3u + 2

Reorder the terms:
-8 + 2u2 = u2 + -3u + 2

Reorder the terms:
-8 + 2u2 = 2 + -3u + u2

Solving
-8 + 2u2 = 2 + -3u + u2

Solving for variable 'u'.

Reorder the terms:
-8 + -2 + 3u + 2u2 + -1u2 = 2 + -3u + u2 + -2 + 3u + -1u2

Combine like terms: -8 + -2 = -10
-10 + 3u + 2u2 + -1u2 = 2 + -3u + u2 + -2 + 3u + -1u2

Combine like terms: 2u2 + -1u2 = 1u2
-10 + 3u + 1u2 = 2 + -3u + u2 + -2 + 3u + -1u2

Reorder the terms:
-10 + 3u + 1u2 = 2 + -2 + -3u + 3u + u2 + -1u2

Combine like terms: 2 + -2 = 0
-10 + 3u + 1u2 = 0 + -3u + 3u + u2 + -1u2
-10 + 3u + 1u2 = -3u + 3u + u2 + -1u2

Combine like terms: -3u + 3u = 0
-10 + 3u + 1u2 = 0 + u2 + -1u2
-10 + 3u + 1u2 = u2 + -1u2

Combine like terms: u2 + -1u2 = 0
-10 + 3u + 1u2 = 0

Factor a trinomial.
(-5 + -1u)(2 + -1u) = 0


Subproblem 1
Set the factor '(-5 + -1u)' equal to zero and attempt to solve:

Simplifying
-5 + -1u = 0

Solving
-5 + -1u = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1u = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1u = 0 + 5
-1u = 0 + 5

Combine like terms: 0 + 5 = 5
-1u = 5

Divide each side by '-1'.
u = -5

Simplifying
u = -5

Subproblem 2
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
Solution
u = {-5, 2}

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