2(9x-1)7(x+6)=-60

Solution for 2(9x-1)7(x+6)=-60 equation:

Simplifying
2(9x + -1) * 7(x + 6) = -60

Reorder the terms:
2(-1 + 9x) * 7(x + 6) = -60

Reorder the terms:
2(-1 + 9x) * 7(6 + x) = -60

Reorder the terms for easier multiplication:
2 * 7(-1 + 9x)(6 + x) = -60

Multiply 2 * 7
14(-1 + 9x)(6 + x) = -60

Multiply (-1 + 9x) * (6 + x)
14(-1(6 + x) + 9x * (6 + x)) = -60
14((6 * -1 + x * -1) + 9x * (6 + x)) = -60
14((-6 + -1x) + 9x * (6 + x)) = -60
14(-6 + -1x + (6 * 9x + x * 9x)) = -60
14(-6 + -1x + (54x + 9x2)) = -60

Combine like terms: -1x + 54x = 53x
14(-6 + 53x + 9x2) = -60
(-6 * 14 + 53x * 14 + 9x2 * 14) = -60
(-84 + 742x + 126x2) = -60

Solving
-84 + 742x + 126x2 = -60

Solving for variable 'x'.

Reorder the terms:
-84 + 60 + 742x + 126x2 = -60 + 60

Combine like terms: -84 + 60 = -24
-24 + 742x + 126x2 = -60 + 60

Combine like terms: -60 + 60 = 0
-24 + 742x + 126x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 371x + 63x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + 371x + 63x2)' equal to zero and attempt to solve:

Simplifying
-12 + 371x + 63x2 = 0

Solving
-12 + 371x + 63x2 = 0

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

Divide each side by '63'.
-0.1904761905 + 5.888888889x + x2 = 0

Move the constant term to the right:

Add '0.1904761905' to each side of the equation.
-0.1904761905 + 5.888888889x + 0.1904761905 + x2 = 0 + 0.1904761905

Reorder the terms:
-0.1904761905 + 0.1904761905 + 5.888888889x + x2 = 0 + 0.1904761905

Combine like terms: -0.1904761905 + 0.1904761905 = 0.0000000000
0.0000000000 + 5.888888889x + x2 = 0 + 0.1904761905
5.888888889x + x2 = 0 + 0.1904761905

Combine like terms: 0 + 0.1904761905 = 0.1904761905
5.888888889x + x2 = 0.1904761905

The x term is 5.888888889x.  Take half its coefficient (2.944444445).
Square it (8.669753090) and add it to both sides.

Add '8.669753090' to each side of the equation.
5.888888889x + 8.669753090 + x2 = 0.1904761905 + 8.669753090

Reorder the terms:
8.669753090 + 5.888888889x + x2 = 0.1904761905 + 8.669753090

Combine like terms: 0.1904761905 + 8.669753090 = 8.8602292805
8.669753090 + 5.888888889x + x2 = 8.8602292805

Factor a perfect square on the left side:
(x + 2.944444445)(x + 2.944444445) = 8.8602292805

Calculate the square root of the right side: 2.976613727

Break this problem into two subproblems by setting 
(x + 2.944444445) equal to 2.976613727 and -2.976613727.

Subproblem 1
x + 2.944444445 = 2.976613727

Simplifying
x + 2.944444445 = 2.976613727

Reorder the terms:
2.944444445 + x = 2.976613727

Solving
2.944444445 + x = 2.976613727

Solving for variable 'x'.

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

Add '-2.944444445' to each side of the equation.
2.944444445 + -2.944444445 + x = 2.976613727 + -2.944444445

Combine like terms: 2.944444445 + -2.944444445 = 0.000000000
0.000000000 + x = 2.976613727 + -2.944444445
x = 2.976613727 + -2.944444445

Combine like terms: 2.976613727 + -2.944444445 = 0.032169282
x = 0.032169282

Simplifying
x = 0.032169282

Subproblem 2
x + 2.944444445 = -2.976613727

Simplifying
x + 2.944444445 = -2.976613727

Reorder the terms:
2.944444445 + x = -2.976613727

Solving
2.944444445 + x = -2.976613727

Solving for variable 'x'.

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

Add '-2.944444445' to each side of the equation.
2.944444445 + -2.944444445 + x = -2.976613727 + -2.944444445

Combine like terms: 2.944444445 + -2.944444445 = 0.000000000
0.000000000 + x = -2.976613727 + -2.944444445
x = -2.976613727 + -2.944444445

Combine like terms: -2.976613727 + -2.944444445 = -5.921058172
x = -5.921058172

Simplifying
x = -5.921058172

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.032169282, -5.921058172}
Solution
x = {0.032169282, -5.921058172}