6u^2+6u-24=0

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Solution for 6u^2+6u-24=0 equation: 


Simplifying
6u2 + 6u + -24 = 0

Reorder the terms:
-24 + 6u + 6u2 = 0

Solving
-24 + 6u + 6u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + u + u2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-4 + u + u2)' equal to zero and attempt to solve:

Simplifying
-4 + u + u2 = 0

Solving
-4 + u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + u + 4 + u2 = 0 + 4

Reorder the terms:
-4 + 4 + u + u2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + u + u2 = 0 + 4
u + u2 = 0 + 4

Combine like terms: 0 + 4 = 4
u + u2 = 4

The u term is u.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
u + 0.25 + u2 = 4 + 0.25

Reorder the terms:
0.25 + u + u2 = 4 + 0.25

Combine like terms: 4 + 0.25 = 4.25
0.25 + u + u2 = 4.25

Factor a perfect square on the left side:
(u + 0.5)(u + 0.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(u + 0.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
u + 0.5 = 2.061552813

Simplifying
u + 0.5 = 2.061552813

Reorder the terms:
0.5 + u = 2.061552813

Solving
0.5 + u = 2.061552813

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = 2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = 2.061552813 + -0.5
u = 2.061552813 + -0.5

Combine like terms: 2.061552813 + -0.5 = 1.561552813
u = 1.561552813

Simplifying
u = 1.561552813


Subproblem 2
u + 0.5 = -2.061552813

Simplifying
u + 0.5 = -2.061552813

Reorder the terms:
0.5 + u = -2.061552813

Solving
0.5 + u = -2.061552813

Solving for variable 'u'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + u = -2.061552813 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + u = -2.061552813 + -0.5
u = -2.061552813 + -0.5

Combine like terms: -2.061552813 + -0.5 = -2.561552813
u = -2.561552813

Simplifying
u = -2.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.561552813, -2.561552813}
Solution
u = {1.561552813, -2.561552813}

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