4a(a+4)-6(a+5)=

Solution for 4a(a+4)-6(a+5)= equation:

Simplifying
4a(a + 4) + -6(a + 5) = 0

Reorder the terms:
4a(4 + a) + -6(a + 5) = 0
(4 * 4a + a * 4a) + -6(a + 5) = 0
(16a + 4a2) + -6(a + 5) = 0

Reorder the terms:
16a + 4a2 + -6(5 + a) = 0
16a + 4a2 + (5 * -6 + a * -6) = 0
16a + 4a2 + (-30 + -6a) = 0

Reorder the terms:
-30 + 16a + -6a + 4a2 = 0

Combine like terms: 16a + -6a = 10a
-30 + 10a + 4a2 = 0

Solving
-30 + 10a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 5a + 2a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + 5a + 2a2)' equal to zero and attempt to solve:

Simplifying
-15 + 5a + 2a2 = 0

Solving
-15 + 5a + 2a2 = 0

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

Divide each side by '2'.
-7.5 + 2.5a + a2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 2.5a + 7.5 + a2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 2.5a + a2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 2.5a + a2 = 0 + 7.5
2.5a + a2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
2.5a + a2 = 7.5

The a term is 2.5a.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5a + 1.5625 + a2 = 7.5 + 1.5625

Reorder the terms:
1.5625 + 2.5a + a2 = 7.5 + 1.5625

Combine like terms: 7.5 + 1.5625 = 9.0625
1.5625 + 2.5a + a2 = 9.0625

Factor a perfect square on the left side:
(a + 1.25)(a + 1.25) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(a + 1.25) equal to 3.010398645 and -3.010398645.

Subproblem 1
a + 1.25 = 3.010398645

Simplifying
a + 1.25 = 3.010398645

Reorder the terms:
1.25 + a = 3.010398645

Solving
1.25 + a = 3.010398645

Solving for variable 'a'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + a = 3.010398645 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + a = 3.010398645 + -1.25
a = 3.010398645 + -1.25

Combine like terms: 3.010398645 + -1.25 = 1.760398645
a = 1.760398645

Simplifying
a = 1.760398645

Subproblem 2
a + 1.25 = -3.010398645

Simplifying
a + 1.25 = -3.010398645

Reorder the terms:
1.25 + a = -3.010398645

Solving
1.25 + a = -3.010398645

Solving for variable 'a'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + a = -3.010398645 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + a = -3.010398645 + -1.25
a = -3.010398645 + -1.25

Combine like terms: -3.010398645 + -1.25 = -4.260398645
a = -4.260398645

Simplifying
a = -4.260398645

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.760398645, -4.260398645}
Solution
a = {1.760398645, -4.260398645}