4(5a+3)9a=-3(a-1)+31

Solution for 4(5a+3)9a=-3(a-1)+31 equation:

Simplifying
4(5a + 3) * 9a = -3(a + -1) + 31

Reorder the terms:
4(3 + 5a) * 9a = -3(a + -1) + 31

Reorder the terms for easier multiplication:
4 * 9a(3 + 5a) = -3(a + -1) + 31

Multiply 4 * 9
36a(3 + 5a) = -3(a + -1) + 31
(3 * 36a + 5a * 36a) = -3(a + -1) + 31
(108a + 180a2) = -3(a + -1) + 31

Reorder the terms:
108a + 180a2 = -3(-1 + a) + 31
108a + 180a2 = (-1 * -3 + a * -3) + 31
108a + 180a2 = (3 + -3a) + 31

Reorder the terms:
108a + 180a2 = 3 + 31 + -3a

Combine like terms: 3 + 31 = 34
108a + 180a2 = 34 + -3a

Solving
108a + 180a2 = 34 + -3a

Solving for variable 'a'.

Reorder the terms:
-34 + 108a + 3a + 180a2 = 34 + -3a + -34 + 3a

Combine like terms: 108a + 3a = 111a
-34 + 111a + 180a2 = 34 + -3a + -34 + 3a

Reorder the terms:
-34 + 111a + 180a2 = 34 + -34 + -3a + 3a

Combine like terms: 34 + -34 = 0
-34 + 111a + 180a2 = 0 + -3a + 3a
-34 + 111a + 180a2 = -3a + 3a

Combine like terms: -3a + 3a = 0
-34 + 111a + 180a2 = 0

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

Divide each side by '180'.
-0.1888888889 + 0.6166666667a + a2 = 0.0

Move the constant term to the right:

Add '0.1888888889' to each side of the equation.
-0.1888888889 + 0.6166666667a + 0.1888888889 + a2 = 0.0 + 0.1888888889

Reorder the terms:
-0.1888888889 + 0.1888888889 + 0.6166666667a + a2 = 0.0 + 0.1888888889

Combine like terms: -0.1888888889 + 0.1888888889 = 0.0000000000
0.0000000000 + 0.6166666667a + a2 = 0.0 + 0.1888888889
0.6166666667a + a2 = 0.0 + 0.1888888889

Combine like terms: 0.0 + 0.1888888889 = 0.1888888889
0.6166666667a + a2 = 0.1888888889

The a term is 0.6166666667a.  Take half its coefficient (0.3083333334).
Square it (0.09506944449) and add it to both sides.

Add '0.09506944449' to each side of the equation.
0.6166666667a + 0.09506944449 + a2 = 0.1888888889 + 0.09506944449

Reorder the terms:
0.09506944449 + 0.6166666667a + a2 = 0.1888888889 + 0.09506944449

Combine like terms: 0.1888888889 + 0.09506944449 = 0.28395833339
0.09506944449 + 0.6166666667a + a2 = 0.28395833339

Factor a perfect square on the left side:
(a + 0.3083333334)(a + 0.3083333334) = 0.28395833339

Calculate the square root of the right side: 0.532877409

Break this problem into two subproblems by setting 
(a + 0.3083333334) equal to 0.532877409 and -0.532877409.

Subproblem 1
a + 0.3083333334 = 0.532877409

Simplifying
a + 0.3083333334 = 0.532877409

Reorder the terms:
0.3083333334 + a = 0.532877409

Solving
0.3083333334 + a = 0.532877409

Solving for variable 'a'.

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

Add '-0.3083333334' to each side of the equation.
0.3083333334 + -0.3083333334 + a = 0.532877409 + -0.3083333334

Combine like terms: 0.3083333334 + -0.3083333334 = 0.0000000000
0.0000000000 + a = 0.532877409 + -0.3083333334
a = 0.532877409 + -0.3083333334

Combine like terms: 0.532877409 + -0.3083333334 = 0.2245440756
a = 0.2245440756

Simplifying
a = 0.2245440756

Subproblem 2
a + 0.3083333334 = -0.532877409

Simplifying
a + 0.3083333334 = -0.532877409

Reorder the terms:
0.3083333334 + a = -0.532877409

Solving
0.3083333334 + a = -0.532877409

Solving for variable 'a'.

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

Add '-0.3083333334' to each side of the equation.
0.3083333334 + -0.3083333334 + a = -0.532877409 + -0.3083333334

Combine like terms: 0.3083333334 + -0.3083333334 = 0.0000000000
0.0000000000 + a = -0.532877409 + -0.3083333334
a = -0.532877409 + -0.3083333334

Combine like terms: -0.532877409 + -0.3083333334 = -0.8412107424
a = -0.8412107424

Simplifying
a = -0.8412107424

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.2245440756, -0.8412107424}