5a-9=(-3a+7)5a

Solution for 5a-9=(-3a+7)5a equation:

Simplifying
5a + -9 = (-3a + 7) * 5a

Reorder the terms:
-9 + 5a = (-3a + 7) * 5a

Reorder the terms:
-9 + 5a = (7 + -3a) * 5a

Reorder the terms for easier multiplication:
-9 + 5a = 5a(7 + -3a)
-9 + 5a = (7 * 5a + -3a * 5a)
-9 + 5a = (35a + -15a2)

Solving
-9 + 5a = 35a + -15a2

Solving for variable 'a'.

Combine like terms: 5a + -35a = -30a
-9 + -30a + 15a2 = 35a + -15a2 + -35a + 15a2

Reorder the terms:
-9 + -30a + 15a2 = 35a + -35a + -15a2 + 15a2

Combine like terms: 35a + -35a = 0
-9 + -30a + 15a2 = 0 + -15a2 + 15a2
-9 + -30a + 15a2 = -15a2 + 15a2

Combine like terms: -15a2 + 15a2 = 0
-9 + -30a + 15a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -10a + 5a2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -10a + 5a2)' equal to zero and attempt to solve:

Simplifying
-3 + -10a + 5a2 = 0

Solving
-3 + -10a + 5a2 = 0

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

Divide each side by '5'.
-0.6 + -2a + a2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2a + 0.6 + a2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2a + a2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2a + a2 = 0 + 0.6
-2a + a2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2a + a2 = 0.6

The a term is -2a.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2a + 1 + a2 = 0.6 + 1

Reorder the terms:
1 + -2a + a2 = 0.6 + 1

Combine like terms: 0.6 + 1 = 1.6
1 + -2a + a2 = 1.6

Factor a perfect square on the left side:
(a + -1)(a + -1) = 1.6

Calculate the square root of the right side: 1.264911064

Break this problem into two subproblems by setting 
(a + -1) equal to 1.264911064 and -1.264911064.

Subproblem 1
a + -1 = 1.264911064

Simplifying
a + -1 = 1.264911064

Reorder the terms:
-1 + a = 1.264911064

Solving
-1 + a = 1.264911064

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = 1.264911064 + 1

Combine like terms: -1 + 1 = 0
0 + a = 1.264911064 + 1
a = 1.264911064 + 1

Combine like terms: 1.264911064 + 1 = 2.264911064
a = 2.264911064

Simplifying
a = 2.264911064

Subproblem 2
a + -1 = -1.264911064

Simplifying
a + -1 = -1.264911064

Reorder the terms:
-1 + a = -1.264911064

Solving
-1 + a = -1.264911064

Solving for variable 'a'.

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

Add '1' to each side of the equation.
-1 + 1 + a = -1.264911064 + 1

Combine like terms: -1 + 1 = 0
0 + a = -1.264911064 + 1
a = -1.264911064 + 1

Combine like terms: -1.264911064 + 1 = -0.264911064
a = -0.264911064

Simplifying
a = -0.264911064

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.264911064, -0.264911064}
Solution
a = {2.264911064, -0.264911064}