5(a-6)(a+3)=a^2-5a+6

Solution for 5(a-6)(a+3)=a^2-5a+6 equation:

Simplifying
5(a + -6)(a + 3) = a2 + -5a + 6

Reorder the terms:
5(-6 + a)(a + 3) = a2 + -5a + 6

Reorder the terms:
5(-6 + a)(3 + a) = a2 + -5a + 6

Multiply (-6 + a) * (3 + a)
5(-6(3 + a) + a(3 + a)) = a2 + -5a + 6
5((3 * -6 + a * -6) + a(3 + a)) = a2 + -5a + 6
5((-18 + -6a) + a(3 + a)) = a2 + -5a + 6
5(-18 + -6a + (3 * a + a * a)) = a2 + -5a + 6
5(-18 + -6a + (3a + a2)) = a2 + -5a + 6

Combine like terms: -6a + 3a = -3a
5(-18 + -3a + a2) = a2 + -5a + 6
(-18 * 5 + -3a * 5 + a2 * 5) = a2 + -5a + 6
(-90 + -15a + 5a2) = a2 + -5a + 6

Reorder the terms:
-90 + -15a + 5a2 = 6 + -5a + a2

Solving
-90 + -15a + 5a2 = 6 + -5a + a2

Solving for variable 'a'.

Reorder the terms:
-90 + -6 + -15a + 5a + 5a2 + -1a2 = 6 + -5a + a2 + -6 + 5a + -1a2

Combine like terms: -90 + -6 = -96
-96 + -15a + 5a + 5a2 + -1a2 = 6 + -5a + a2 + -6 + 5a + -1a2

Combine like terms: -15a + 5a = -10a
-96 + -10a + 5a2 + -1a2 = 6 + -5a + a2 + -6 + 5a + -1a2

Combine like terms: 5a2 + -1a2 = 4a2
-96 + -10a + 4a2 = 6 + -5a + a2 + -6 + 5a + -1a2

Reorder the terms:
-96 + -10a + 4a2 = 6 + -6 + -5a + 5a + a2 + -1a2

Combine like terms: 6 + -6 = 0
-96 + -10a + 4a2 = 0 + -5a + 5a + a2 + -1a2
-96 + -10a + 4a2 = -5a + 5a + a2 + -1a2

Combine like terms: -5a + 5a = 0
-96 + -10a + 4a2 = 0 + a2 + -1a2
-96 + -10a + 4a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-96 + -10a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + -5a + 2a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-48 + -5a + 2a2)' equal to zero and attempt to solve:

Simplifying
-48 + -5a + 2a2 = 0

Solving
-48 + -5a + 2a2 = 0

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

Divide each side by '2'.
-24 + -2.5a + a2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -2.5a + 24 + a2 = 0 + 24

Reorder the terms:
-24 + 24 + -2.5a + a2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -2.5a + a2 = 0 + 24
-2.5a + a2 = 0 + 24

Combine like terms: 0 + 24 = 24
-2.5a + a2 = 24

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 = 24 + 1.5625

Reorder the terms:
1.5625 + -2.5a + a2 = 24 + 1.5625

Combine like terms: 24 + 1.5625 = 25.5625
1.5625 + -2.5a + a2 = 25.5625

Factor a perfect square on the left side:
(a + -1.25)(a + -1.25) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(a + -1.25) equal to 5.055937104 and -5.055937104.

Subproblem 1
a + -1.25 = 5.055937104

Simplifying
a + -1.25 = 5.055937104

Reorder the terms:
-1.25 + a = 5.055937104

Solving
-1.25 + a = 5.055937104

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 = 5.055937104 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + a = 5.055937104 + 1.25
a = 5.055937104 + 1.25

Combine like terms: 5.055937104 + 1.25 = 6.305937104
a = 6.305937104

Simplifying
a = 6.305937104

Subproblem 2
a + -1.25 = -5.055937104

Simplifying
a + -1.25 = -5.055937104

Reorder the terms:
-1.25 + a = -5.055937104

Solving
-1.25 + a = -5.055937104

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 = -5.055937104 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + a = -5.055937104 + 1.25
a = -5.055937104 + 1.25

Combine like terms: -5.055937104 + 1.25 = -3.805937104
a = -3.805937104

Simplifying
a = -3.805937104

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {6.305937104, -3.805937104}
Solution
a = {6.305937104, -3.805937104}