(u-2)(u^2+2u+4)-3u+8=0

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Solution for (u-2)(u^2+2u+4)-3u+8=0 equation: 


Simplifying
(u + -2)(u2 + 2u + 4) + -3u + 8 = 0

Reorder the terms:
(-2 + u)(u2 + 2u + 4) + -3u + 8 = 0

Reorder the terms:
(-2 + u)(4 + 2u + u2) + -3u + 8 = 0

Multiply (-2 + u) * (4 + 2u + u2)
(-2(4 + 2u + u2) + u(4 + 2u + u2)) + -3u + 8 = 0
((4 * -2 + 2u * -2 + u2 * -2) + u(4 + 2u + u2)) + -3u + 8 = 0
((-8 + -4u + -2u2) + u(4 + 2u + u2)) + -3u + 8 = 0
(-8 + -4u + -2u2 + (4 * u + 2u * u + u2 * u)) + -3u + 8 = 0
(-8 + -4u + -2u2 + (4u + 2u2 + u3)) + -3u + 8 = 0

Reorder the terms:
(-8 + -4u + 4u + -2u2 + 2u2 + u3) + -3u + 8 = 0

Combine like terms: -4u + 4u = 0
(-8 + 0 + -2u2 + 2u2 + u3) + -3u + 8 = 0
(-8 + -2u2 + 2u2 + u3) + -3u + 8 = 0

Combine like terms: -2u2 + 2u2 = 0
(-8 + 0 + u3) + -3u + 8 = 0
(-8 + u3) + -3u + 8 = 0

Reorder the terms:
-8 + 8 + -3u + u3 = 0

Combine like terms: -8 + 8 = 0
0 + -3u + u3 = 0
-3u + u3 = 0

Solving
-3u + u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u'.
u(-3 + u2) = 0


Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0

Subproblem 2
Set the factor '(-3 + u2)' equal to zero and attempt to solve:

Simplifying
-3 + u2 = 0

Solving
-3 + u2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + u2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + u2 = 0 + 3
u2 = 0 + 3

Combine like terms: 0 + 3 = 3
u2 = 3

Simplifying
u2 = 3

Take the square root of each side:
u = {-1.732050808, 1.732050808}
Solution
u = {0, -1.732050808, 1.732050808}

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