4a(a-3)=5

Solution for 4a(a-3)=5 equation:

Simplifying
4a(a + -3) = 5

Reorder the terms:
4a(-3 + a) = 5
(-3 * 4a + a * 4a) = 5
(-12a + 4a2) = 5

Solving
-12a + 4a2 = 5

Solving for variable 'a'.

Reorder the terms:
-5 + -12a + 4a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -12a + 4a2 = 0

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

Divide each side by '4'.
-1.25 + -3a + a2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -3a + 1.25 + a2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -3a + a2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -3a + a2 = 0 + 1.25
-3a + a2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-3a + a2 = 1.25

The a term is -3a.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3a + 2.25 + a2 = 1.25 + 2.25

Reorder the terms:
2.25 + -3a + a2 = 1.25 + 2.25

Combine like terms: 1.25 + 2.25 = 3.5
2.25 + -3a + a2 = 3.5

Factor a perfect square on the left side:
(a + -1.5)(a + -1.5) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(a + -1.5) equal to 1.870828693 and -1.870828693.

Subproblem 1
a + -1.5 = 1.870828693

Simplifying
a + -1.5 = 1.870828693

Reorder the terms:
-1.5 + a = 1.870828693

Solving
-1.5 + a = 1.870828693

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = 1.870828693 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = 1.870828693 + 1.5
a = 1.870828693 + 1.5

Combine like terms: 1.870828693 + 1.5 = 3.370828693
a = 3.370828693

Simplifying
a = 3.370828693

Subproblem 2
a + -1.5 = -1.870828693

Simplifying
a + -1.5 = -1.870828693

Reorder the terms:
-1.5 + a = -1.870828693

Solving
-1.5 + a = -1.870828693

Solving for variable 'a'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + a = -1.870828693 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + a = -1.870828693 + 1.5
a = -1.870828693 + 1.5

Combine like terms: -1.870828693 + 1.5 = -0.370828693
a = -0.370828693

Simplifying
a = -0.370828693

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.370828693, -0.370828693}