4a(a-1)=30

Solution for 4a(a-1)=30 equation:

Simplifying
4a(a + -1) = 30

Reorder the terms:
4a(-1 + a) = 30
(-1 * 4a + a * 4a) = 30
(-4a + 4a2) = 30

Solving
-4a + 4a2 = 30

Solving for variable 'a'.

Reorder the terms:
-30 + -4a + 4a2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -4a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -2a + 2a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + -2a + 2a2)' equal to zero and attempt to solve:

Simplifying
-15 + -2a + 2a2 = 0

Solving
-15 + -2a + 2a2 = 0

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

Divide each side by '2'.
-7.5 + -1a + a2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -1a + 7.5 + a2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -1a + a2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -1a + a2 = 0 + 7.5
-1a + a2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-1a + a2 = 7.5

The a term is -1a.  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.
-1a + 0.25 + a2 = 7.5 + 0.25

Reorder the terms:
0.25 + -1a + a2 = 7.5 + 0.25

Combine like terms: 7.5 + 0.25 = 7.75
0.25 + -1a + a2 = 7.75

Factor a perfect square on the left side:
(a + -0.5)(a + -0.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(a + -0.5) equal to 2.783882181 and -2.783882181.

Subproblem 1
a + -0.5 = 2.783882181

Simplifying
a + -0.5 = 2.783882181

Reorder the terms:
-0.5 + a = 2.783882181

Solving
-0.5 + a = 2.783882181

Solving for variable 'a'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + a = 2.783882181 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = 2.783882181 + 0.5
a = 2.783882181 + 0.5

Combine like terms: 2.783882181 + 0.5 = 3.283882181
a = 3.283882181

Simplifying
a = 3.283882181

Subproblem 2
a + -0.5 = -2.783882181

Simplifying
a + -0.5 = -2.783882181

Reorder the terms:
-0.5 + a = -2.783882181

Solving
-0.5 + a = -2.783882181

Solving for variable 'a'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + a = -2.783882181 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + a = -2.783882181 + 0.5
a = -2.783882181 + 0.5

Combine like terms: -2.783882181 + 0.5 = -2.283882181
a = -2.283882181

Simplifying
a = -2.283882181

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.283882181, -2.283882181}
Solution
a = {3.283882181, -2.283882181}