(6x+5)(10x+4)=140

Solution for (6x+5)(10x+4)=140 equation:

Simplifying
(6x + 5)(10x + 4) = 140

Reorder the terms:
(5 + 6x)(10x + 4) = 140

Reorder the terms:
(5 + 6x)(4 + 10x) = 140

Multiply (5 + 6x) * (4 + 10x)
(5(4 + 10x) + 6x * (4 + 10x)) = 140
((4 * 5 + 10x * 5) + 6x * (4 + 10x)) = 140
((20 + 50x) + 6x * (4 + 10x)) = 140
(20 + 50x + (4 * 6x + 10x * 6x)) = 140
(20 + 50x + (24x + 60x2)) = 140

Combine like terms: 50x + 24x = 74x
(20 + 74x + 60x2) = 140

Solving
20 + 74x + 60x2 = 140

Solving for variable 'x'.

Reorder the terms:
20 + -140 + 74x + 60x2 = 140 + -140

Combine like terms: 20 + -140 = -120
-120 + 74x + 60x2 = 140 + -140

Combine like terms: 140 + -140 = 0
-120 + 74x + 60x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + 37x + 30x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-60 + 37x + 30x2)' equal to zero and attempt to solve:

Simplifying
-60 + 37x + 30x2 = 0

Solving
-60 + 37x + 30x2 = 0

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

Divide each side by '30'.
-2 + 1.233333333x + x2 = 0.0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.233333333x + 2 + x2 = 0.0 + 2

Reorder the terms:
-2 + 2 + 1.233333333x + x2 = 0.0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.233333333x + x2 = 0.0 + 2
1.233333333x + x2 = 0.0 + 2

Combine like terms: 0.0 + 2 = 2
1.233333333x + x2 = 2

The x term is 1.233333333x.  Take half its coefficient (0.6166666665).
Square it (0.3802777776) and add it to both sides.

Add '0.3802777776' to each side of the equation.
1.233333333x + 0.3802777776 + x2 = 2 + 0.3802777776

Reorder the terms:
0.3802777776 + 1.233333333x + x2 = 2 + 0.3802777776

Combine like terms: 2 + 0.3802777776 = 2.3802777776
0.3802777776 + 1.233333333x + x2 = 2.3802777776

Factor a perfect square on the left side:
(x + 0.6166666665)(x + 0.6166666665) = 2.3802777776

Calculate the square root of the right side: 1.542814888

Break this problem into two subproblems by setting 
(x + 0.6166666665) equal to 1.542814888 and -1.542814888.

Subproblem 1
x + 0.6166666665 = 1.542814888

Simplifying
x + 0.6166666665 = 1.542814888

Reorder the terms:
0.6166666665 + x = 1.542814888

Solving
0.6166666665 + x = 1.542814888

Solving for variable 'x'.

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

Add '-0.6166666665' to each side of the equation.
0.6166666665 + -0.6166666665 + x = 1.542814888 + -0.6166666665

Combine like terms: 0.6166666665 + -0.6166666665 = 0.0000000000
0.0000000000 + x = 1.542814888 + -0.6166666665
x = 1.542814888 + -0.6166666665

Combine like terms: 1.542814888 + -0.6166666665 = 0.9261482215
x = 0.9261482215

Simplifying
x = 0.9261482215

Subproblem 2
x + 0.6166666665 = -1.542814888

Simplifying
x + 0.6166666665 = -1.542814888

Reorder the terms:
0.6166666665 + x = -1.542814888

Solving
0.6166666665 + x = -1.542814888

Solving for variable 'x'.

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

Add '-0.6166666665' to each side of the equation.
0.6166666665 + -0.6166666665 + x = -1.542814888 + -0.6166666665

Combine like terms: 0.6166666665 + -0.6166666665 = 0.0000000000
0.0000000000 + x = -1.542814888 + -0.6166666665
x = -1.542814888 + -0.6166666665

Combine like terms: -1.542814888 + -0.6166666665 = -2.1594815545
x = -2.1594815545

Simplifying
x = -2.1594815545

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9261482215, -2.1594815545}
Solution
x = {0.9261482215, -2.1594815545}