5u^2-75u-900=0

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Solution for 5u^2-75u-900=0 equation: 


Simplifying
5u2 + -75u + -900 = 0

Reorder the terms:
-900 + -75u + 5u2 = 0

Solving
-900 + -75u + 5u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-180 + -15u + u2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-180 + -15u + u2)' equal to zero and attempt to solve:

Simplifying
-180 + -15u + u2 = 0

Solving
-180 + -15u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + -15u + 180 + u2 = 0 + 180

Reorder the terms:
-180 + 180 + -15u + u2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -15u + u2 = 0 + 180
-15u + u2 = 0 + 180

Combine like terms: 0 + 180 = 180
-15u + u2 = 180

The u term is -15u.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15u + 56.25 + u2 = 180 + 56.25

Reorder the terms:
56.25 + -15u + u2 = 180 + 56.25

Combine like terms: 180 + 56.25 = 236.25
56.25 + -15u + u2 = 236.25

Factor a perfect square on the left side:
(u + -7.5)(u + -7.5) = 236.25

Calculate the square root of the right side: 15.370426149

Break this problem into two subproblems by setting 
(u + -7.5) equal to 15.370426149 and -15.370426149.


Subproblem 1
u + -7.5 = 15.370426149

Simplifying
u + -7.5 = 15.370426149

Reorder the terms:
-7.5 + u = 15.370426149

Solving
-7.5 + u = 15.370426149

Solving for variable 'u'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + u = 15.370426149 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + u = 15.370426149 + 7.5
u = 15.370426149 + 7.5

Combine like terms: 15.370426149 + 7.5 = 22.870426149
u = 22.870426149

Simplifying
u = 22.870426149


Subproblem 2
u + -7.5 = -15.370426149

Simplifying
u + -7.5 = -15.370426149

Reorder the terms:
-7.5 + u = -15.370426149

Solving
-7.5 + u = -15.370426149

Solving for variable 'u'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + u = -15.370426149 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + u = -15.370426149 + 7.5
u = -15.370426149 + 7.5

Combine like terms: -15.370426149 + 7.5 = -7.870426149
u = -7.870426149

Simplifying
u = -7.870426149


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {22.870426149, -7.870426149}
Solution
u = {22.870426149, -7.870426149}

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