5a-8=7(a+1)16a+4

Solution for 5a-8=7(a+1)16a+4 equation:

Simplifying
5a + -8 = 7(a + 1) * 16a + 4

Reorder the terms:
-8 + 5a = 7(a + 1) * 16a + 4

Reorder the terms:
-8 + 5a = 7(1 + a) * 16a + 4

Reorder the terms for easier multiplication:
-8 + 5a = 7 * 16a(1 + a) + 4

Multiply 7 * 16
-8 + 5a = 112a(1 + a) + 4
-8 + 5a = (1 * 112a + a * 112a) + 4
-8 + 5a = (112a + 112a2) + 4

Reorder the terms:
-8 + 5a = 4 + 112a + 112a2

Solving
-8 + 5a = 4 + 112a + 112a2

Solving for variable 'a'.

Reorder the terms:
-8 + -4 + 5a + -112a + -112a2 = 4 + 112a + 112a2 + -4 + -112a + -112a2

Combine like terms: -8 + -4 = -12
-12 + 5a + -112a + -112a2 = 4 + 112a + 112a2 + -4 + -112a + -112a2

Combine like terms: 5a + -112a = -107a
-12 + -107a + -112a2 = 4 + 112a + 112a2 + -4 + -112a + -112a2

Reorder the terms:
-12 + -107a + -112a2 = 4 + -4 + 112a + -112a + 112a2 + -112a2

Combine like terms: 4 + -4 = 0
-12 + -107a + -112a2 = 0 + 112a + -112a + 112a2 + -112a2
-12 + -107a + -112a2 = 112a + -112a + 112a2 + -112a2

Combine like terms: 112a + -112a = 0
-12 + -107a + -112a2 = 0 + 112a2 + -112a2
-12 + -107a + -112a2 = 112a2 + -112a2

Combine like terms: 112a2 + -112a2 = 0
-12 + -107a + -112a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 107a + 112a2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(12 + 107a + 112a2)' equal to zero and attempt to solve:

Simplifying
12 + 107a + 112a2 = 0

Solving
12 + 107a + 112a2 = 0

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

Divide each side by '112'.
0.1071428571 + 0.9553571429a + a2 = 0

Move the constant term to the right:

Add '-0.1071428571' to each side of the equation.
0.1071428571 + 0.9553571429a + -0.1071428571 + a2 = 0 + -0.1071428571

Reorder the terms:
0.1071428571 + -0.1071428571 + 0.9553571429a + a2 = 0 + -0.1071428571

Combine like terms: 0.1071428571 + -0.1071428571 = 0.0000000000
0.0000000000 + 0.9553571429a + a2 = 0 + -0.1071428571
0.9553571429a + a2 = 0 + -0.1071428571

Combine like terms: 0 + -0.1071428571 = -0.1071428571
0.9553571429a + a2 = -0.1071428571

The a term is 0.9553571429a.  Take half its coefficient (0.4776785715).
Square it (0.2281768177) and add it to both sides.

Add '0.2281768177' to each side of the equation.
0.9553571429a + 0.2281768177 + a2 = -0.1071428571 + 0.2281768177

Reorder the terms:
0.2281768177 + 0.9553571429a + a2 = -0.1071428571 + 0.2281768177

Combine like terms: -0.1071428571 + 0.2281768177 = 0.1210339606
0.2281768177 + 0.9553571429a + a2 = 0.1210339606

Factor a perfect square on the left side:
(a + 0.4776785715)(a + 0.4776785715) = 0.1210339606

Calculate the square root of the right side: 0.347899354

Break this problem into two subproblems by setting 
(a + 0.4776785715) equal to 0.347899354 and -0.347899354.

Subproblem 1
a + 0.4776785715 = 0.347899354

Simplifying
a + 0.4776785715 = 0.347899354

Reorder the terms:
0.4776785715 + a = 0.347899354

Solving
0.4776785715 + a = 0.347899354

Solving for variable 'a'.

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

Add '-0.4776785715' to each side of the equation.
0.4776785715 + -0.4776785715 + a = 0.347899354 + -0.4776785715

Combine like terms: 0.4776785715 + -0.4776785715 = 0.0000000000
0.0000000000 + a = 0.347899354 + -0.4776785715
a = 0.347899354 + -0.4776785715

Combine like terms: 0.347899354 + -0.4776785715 = -0.1297792175
a = -0.1297792175

Simplifying
a = -0.1297792175

Subproblem 2
a + 0.4776785715 = -0.347899354

Simplifying
a + 0.4776785715 = -0.347899354

Reorder the terms:
0.4776785715 + a = -0.347899354

Solving
0.4776785715 + a = -0.347899354

Solving for variable 'a'.

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

Add '-0.4776785715' to each side of the equation.
0.4776785715 + -0.4776785715 + a = -0.347899354 + -0.4776785715

Combine like terms: 0.4776785715 + -0.4776785715 = 0.0000000000
0.0000000000 + a = -0.347899354 + -0.4776785715
a = -0.347899354 + -0.4776785715

Combine like terms: -0.347899354 + -0.4776785715 = -0.8255779255
a = -0.8255779255

Simplifying
a = -0.8255779255

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.1297792175, -0.8255779255}
Solution
a = {-0.1297792175, -0.8255779255}