(a*2)+(a+4)7(a-1)=14

Solution for (a*2)+(a+4)7(a-1)=14 equation:

Simplifying
(a * 2) + (a + 4) * 7(a + -1) = 14

Reorder the terms for easier multiplication:
(2a) + (a + 4) * 7(a + -1) = 14

Reorder the terms:
(2a) + (4 + a) * 7(a + -1) = 14

Reorder the terms:
(2a) + (4 + a) * 7(-1 + a) = 14

Reorder the terms for easier multiplication:
(2a) + 7(4 + a)(-1 + a) = 14

Multiply (4 + a) * (-1 + a)
(2a) + 7(4(-1 + a) + a(-1 + a)) = 14
(2a) + 7((-1 * 4 + a * 4) + a(-1 + a)) = 14
(2a) + 7((-4 + 4a) + a(-1 + a)) = 14
(2a) + 7(-4 + 4a + (-1 * a + a * a)) = 14
(2a) + 7(-4 + 4a + (-1a + a2)) = 14

Combine like terms: 4a + -1a = 3a
(2a) + 7(-4 + 3a + a2) = 14
(2a) + (-4 * 7 + 3a * 7 + a2 * 7) = 14
(2a) + (-28 + 21a + 7a2) = 14

Reorder the terms:
-28 + (2a) + 21a + 7a2 = 14

Combine like terms: (2a) + 21a = 23a
-28 + 23a + 7a2 = 14

Solving
-28 + 23a + 7a2 = 14

Solving for variable 'a'.

Reorder the terms:
-28 + -14 + 23a + 7a2 = 14 + -14

Combine like terms: -28 + -14 = -42
-42 + 23a + 7a2 = 14 + -14

Combine like terms: 14 + -14 = 0
-42 + 23a + 7a2 = 0

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

Divide each side by '7'.
-6 + 3.285714286a + a2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3.285714286a + 6 + a2 = 0 + 6

Reorder the terms:
-6 + 6 + 3.285714286a + a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3.285714286a + a2 = 0 + 6
3.285714286a + a2 = 0 + 6

Combine like terms: 0 + 6 = 6
3.285714286a + a2 = 6

The a term is 3.285714286a.  Take half its coefficient (1.642857143).
Square it (2.698979592) and add it to both sides.

Add '2.698979592' to each side of the equation.
3.285714286a + 2.698979592 + a2 = 6 + 2.698979592

Reorder the terms:
2.698979592 + 3.285714286a + a2 = 6 + 2.698979592

Combine like terms: 6 + 2.698979592 = 8.698979592
2.698979592 + 3.285714286a + a2 = 8.698979592

Factor a perfect square on the left side:
(a + 1.642857143)(a + 1.642857143) = 8.698979592

Calculate the square root of the right side: 2.94940326

Break this problem into two subproblems by setting 
(a + 1.642857143) equal to 2.94940326 and -2.94940326.

Subproblem 1
a + 1.642857143 = 2.94940326

Simplifying
a + 1.642857143 = 2.94940326

Reorder the terms:
1.642857143 + a = 2.94940326

Solving
1.642857143 + a = 2.94940326

Solving for variable 'a'.

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

Add '-1.642857143' to each side of the equation.
1.642857143 + -1.642857143 + a = 2.94940326 + -1.642857143

Combine like terms: 1.642857143 + -1.642857143 = 0.000000000
0.000000000 + a = 2.94940326 + -1.642857143
a = 2.94940326 + -1.642857143

Combine like terms: 2.94940326 + -1.642857143 = 1.306546117
a = 1.306546117

Simplifying
a = 1.306546117

Subproblem 2
a + 1.642857143 = -2.94940326

Simplifying
a + 1.642857143 = -2.94940326

Reorder the terms:
1.642857143 + a = -2.94940326

Solving
1.642857143 + a = -2.94940326

Solving for variable 'a'.

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

Add '-1.642857143' to each side of the equation.
1.642857143 + -1.642857143 + a = -2.94940326 + -1.642857143

Combine like terms: 1.642857143 + -1.642857143 = 0.000000000
0.000000000 + a = -2.94940326 + -1.642857143
a = -2.94940326 + -1.642857143

Combine like terms: -2.94940326 + -1.642857143 = -4.592260403
a = -4.592260403

Simplifying
a = -4.592260403

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {1.306546117, -4.592260403}