4a(a-5)=10

Solution for 4a(a-5)=10 equation:

Simplifying
4a(a + -5) = 10

Reorder the terms:
4a(-5 + a) = 10
(-5 * 4a + a * 4a) = 10
(-20a + 4a2) = 10

Solving
-20a + 4a2 = 10

Solving for variable 'a'.

Reorder the terms:
-10 + -20a + 4a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -20a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -10a + 2a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -10a + 2a2)' equal to zero and attempt to solve:

Simplifying
-5 + -10a + 2a2 = 0

Solving
-5 + -10a + 2a2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-2.5 + -5a + a2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -5a + 2.5 + a2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -5a + a2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -5a + a2 = 0 + 2.5
-5a + a2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-5a + a2 = 2.5

The a term is -5a.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5a + 6.25 + a2 = 2.5 + 6.25

Reorder the terms:
6.25 + -5a + a2 = 2.5 + 6.25

Combine like terms: 2.5 + 6.25 = 8.75
6.25 + -5a + a2 = 8.75

Factor a perfect square on the left side:
(a + -2.5)(a + -2.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(a + -2.5) equal to 2.958039892 and -2.958039892.

Subproblem 1
a + -2.5 = 2.958039892

Simplifying
a + -2.5 = 2.958039892

Reorder the terms:
-2.5 + a = 2.958039892

Solving
-2.5 + a = 2.958039892

Solving for variable 'a'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + a = 2.958039892 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + a = 2.958039892 + 2.5
a = 2.958039892 + 2.5

Combine like terms: 2.958039892 + 2.5 = 5.458039892
a = 5.458039892

Simplifying
a = 5.458039892

Subproblem 2
a + -2.5 = -2.958039892

Simplifying
a + -2.5 = -2.958039892

Reorder the terms:
-2.5 + a = -2.958039892

Solving
-2.5 + a = -2.958039892

Solving for variable 'a'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + a = -2.958039892 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + a = -2.958039892 + 2.5
a = -2.958039892 + 2.5

Combine like terms: -2.958039892 + 2.5 = -0.458039892
a = -0.458039892

Simplifying
a = -0.458039892

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.458039892, -0.458039892}
Solution
a = {5.458039892, -0.458039892}