10(a+1)14a=9-(4a-1)

Solution for 10(a+1)14a=9-(4a-1) equation:

Simplifying
10(a + 1) * 14a = 9 + -1(4a + -1)

Reorder the terms:
10(1 + a) * 14a = 9 + -1(4a + -1)

Reorder the terms for easier multiplication:
10 * 14a(1 + a) = 9 + -1(4a + -1)

Multiply 10 * 14
140a(1 + a) = 9 + -1(4a + -1)
(1 * 140a + a * 140a) = 9 + -1(4a + -1)
(140a + 140a2) = 9 + -1(4a + -1)

Reorder the terms:
140a + 140a2 = 9 + -1(-1 + 4a)
140a + 140a2 = 9 + (-1 * -1 + 4a * -1)
140a + 140a2 = 9 + (1 + -4a)

Combine like terms: 9 + 1 = 10
140a + 140a2 = 10 + -4a

Solving
140a + 140a2 = 10 + -4a

Solving for variable 'a'.

Reorder the terms:
-10 + 140a + 4a + 140a2 = 10 + -4a + -10 + 4a

Combine like terms: 140a + 4a = 144a
-10 + 144a + 140a2 = 10 + -4a + -10 + 4a

Reorder the terms:
-10 + 144a + 140a2 = 10 + -10 + -4a + 4a

Combine like terms: 10 + -10 = 0
-10 + 144a + 140a2 = 0 + -4a + 4a
-10 + 144a + 140a2 = -4a + 4a

Combine like terms: -4a + 4a = 0
-10 + 144a + 140a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 72a + 70a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 72a + 70a2)' equal to zero and attempt to solve:

Simplifying
-5 + 72a + 70a2 = 0

Solving
-5 + 72a + 70a2 = 0

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

Divide each side by '70'.
-0.07142857143 + 1.028571429a + a2 = 0.0

Move the constant term to the right:

Add '0.07142857143' to each side of the equation.
-0.07142857143 + 1.028571429a + 0.07142857143 + a2 = 0.0 + 0.07142857143

Reorder the terms:
-0.07142857143 + 0.07142857143 + 1.028571429a + a2 = 0.0 + 0.07142857143

Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000
0.00000000000 + 1.028571429a + a2 = 0.0 + 0.07142857143
1.028571429a + a2 = 0.0 + 0.07142857143

Combine like terms: 0.0 + 0.07142857143 = 0.07142857143
1.028571429a + a2 = 0.07142857143

The a term is 1.028571429a.  Take half its coefficient (0.5142857145).
Square it (0.2644897961) and add it to both sides.

Add '0.2644897961' to each side of the equation.
1.028571429a + 0.2644897961 + a2 = 0.07142857143 + 0.2644897961

Reorder the terms:
0.2644897961 + 1.028571429a + a2 = 0.07142857143 + 0.2644897961

Combine like terms: 0.07142857143 + 0.2644897961 = 0.33591836753
0.2644897961 + 1.028571429a + a2 = 0.33591836753

Factor a perfect square on the left side:
(a + 0.5142857145)(a + 0.5142857145) = 0.33591836753

Calculate the square root of the right side: 0.579584651

Break this problem into two subproblems by setting 
(a + 0.5142857145) equal to 0.579584651 and -0.579584651.

Subproblem 1
a + 0.5142857145 = 0.579584651

Simplifying
a + 0.5142857145 = 0.579584651

Reorder the terms:
0.5142857145 + a = 0.579584651

Solving
0.5142857145 + a = 0.579584651

Solving for variable 'a'.

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

Add '-0.5142857145' to each side of the equation.
0.5142857145 + -0.5142857145 + a = 0.579584651 + -0.5142857145

Combine like terms: 0.5142857145 + -0.5142857145 = 0.0000000000
0.0000000000 + a = 0.579584651 + -0.5142857145
a = 0.579584651 + -0.5142857145

Combine like terms: 0.579584651 + -0.5142857145 = 0.0652989365
a = 0.0652989365

Simplifying
a = 0.0652989365

Subproblem 2
a + 0.5142857145 = -0.579584651

Simplifying
a + 0.5142857145 = -0.579584651

Reorder the terms:
0.5142857145 + a = -0.579584651

Solving
0.5142857145 + a = -0.579584651

Solving for variable 'a'.

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

Add '-0.5142857145' to each side of the equation.
0.5142857145 + -0.5142857145 + a = -0.579584651 + -0.5142857145

Combine like terms: 0.5142857145 + -0.5142857145 = 0.0000000000
0.0000000000 + a = -0.579584651 + -0.5142857145
a = -0.579584651 + -0.5142857145

Combine like terms: -0.579584651 + -0.5142857145 = -1.0938703655
a = -1.0938703655

Simplifying
a = -1.0938703655

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.0652989365, -1.0938703655}
Solution
a = {0.0652989365, -1.0938703655}