3u^2=24u-6

Solution for 3u^2=24u-6 equation:

Simplifying
3u2 = 24u + -6

Reorder the terms:
3u2 = -6 + 24u

Solving
3u2 = -6 + 24u

Solving for variable 'u'.

Reorder the terms:
6 + -24u + 3u2 = -6 + 24u + 6 + -24u

Reorder the terms:
6 + -24u + 3u2 = -6 + 6 + 24u + -24u

Combine like terms: -6 + 6 = 0
6 + -24u + 3u2 = 0 + 24u + -24u
6 + -24u + 3u2 = 24u + -24u

Combine like terms: 24u + -24u = 0
6 + -24u + 3u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -8u + u2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -8u + u2)' equal to zero and attempt to solve:

Simplifying
2 + -8u + u2 = 0

Solving
2 + -8u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -8u + -2 + u2 = 0 + -2

Reorder the terms:
2 + -2 + -8u + u2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -8u + u2 = 0 + -2
-8u + u2 = 0 + -2

Combine like terms: 0 + -2 = -2
-8u + u2 = -2

The u term is -8u.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8u + 16 + u2 = -2 + 16

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

Combine like terms: -2 + 16 = 14
16 + -8u + u2 = 14

Factor a perfect square on the left side:
(u + -4)(u + -4) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(u + -4) equal to 3.741657387 and -3.741657387.

Subproblem 1
u + -4 = 3.741657387

Simplifying
u + -4 = 3.741657387

Reorder the terms:
-4 + u = 3.741657387

Solving
-4 + u = 3.741657387

Solving for variable 'u'.

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

Add '4' to each side of the equation.
-4 + 4 + u = 3.741657387 + 4

Combine like terms: -4 + 4 = 0
0 + u = 3.741657387 + 4
u = 3.741657387 + 4

Combine like terms: 3.741657387 + 4 = 7.741657387
u = 7.741657387

Simplifying
u = 7.741657387

Subproblem 2
u + -4 = -3.741657387

Simplifying
u + -4 = -3.741657387

Reorder the terms:
-4 + u = -3.741657387

Solving
-4 + u = -3.741657387

Solving for variable 'u'.

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

Add '4' to each side of the equation.
-4 + 4 + u = -3.741657387 + 4

Combine like terms: -4 + 4 = 0
0 + u = -3.741657387 + 4
u = -3.741657387 + 4

Combine like terms: -3.741657387 + 4 = 0.258342613
u = 0.258342613

Simplifying
u = 0.258342613

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {7.741657387, 0.258342613}
Solution
u = {7.741657387, 0.258342613}