(6x+2)(5x+8)=98

Solution for (6x+2)(5x+8)=98 equation:

Simplifying
(6x + 2)(5x + 8) = 98

Reorder the terms:
(2 + 6x)(5x + 8) = 98

Reorder the terms:
(2 + 6x)(8 + 5x) = 98

Multiply (2 + 6x) * (8 + 5x)
(2(8 + 5x) + 6x * (8 + 5x)) = 98
((8 * 2 + 5x * 2) + 6x * (8 + 5x)) = 98
((16 + 10x) + 6x * (8 + 5x)) = 98
(16 + 10x + (8 * 6x + 5x * 6x)) = 98
(16 + 10x + (48x + 30x2)) = 98

Combine like terms: 10x + 48x = 58x
(16 + 58x + 30x2) = 98

Solving
16 + 58x + 30x2 = 98

Solving for variable 'x'.

Reorder the terms:
16 + -98 + 58x + 30x2 = 98 + -98

Combine like terms: 16 + -98 = -82
-82 + 58x + 30x2 = 98 + -98

Combine like terms: 98 + -98 = 0
-82 + 58x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + 29x + 15x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-41 + 29x + 15x2)' equal to zero and attempt to solve:

Simplifying
-41 + 29x + 15x2 = 0

Solving
-41 + 29x + 15x2 = 0

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

Divide each side by '15'.
-2.733333333 + 1.933333333x + x2 = 0

Move the constant term to the right:

Add '2.733333333' to each side of the equation.
-2.733333333 + 1.933333333x + 2.733333333 + x2 = 0 + 2.733333333

Reorder the terms:
-2.733333333 + 2.733333333 + 1.933333333x + x2 = 0 + 2.733333333

Combine like terms: -2.733333333 + 2.733333333 = 0.000000000
0.000000000 + 1.933333333x + x2 = 0 + 2.733333333
1.933333333x + x2 = 0 + 2.733333333

Combine like terms: 0 + 2.733333333 = 2.733333333
1.933333333x + x2 = 2.733333333

The x term is 1.933333333x.  Take half its coefficient (0.9666666665).
Square it (0.9344444441) and add it to both sides.

Add '0.9344444441' to each side of the equation.
1.933333333x + 0.9344444441 + x2 = 2.733333333 + 0.9344444441

Reorder the terms:
0.9344444441 + 1.933333333x + x2 = 2.733333333 + 0.9344444441

Combine like terms: 2.733333333 + 0.9344444441 = 3.6677777771
0.9344444441 + 1.933333333x + x2 = 3.6677777771

Factor a perfect square on the left side:
(x + 0.9666666665)(x + 0.9666666665) = 3.6677777771

Calculate the square root of the right side: 1.915144323

Break this problem into two subproblems by setting 
(x + 0.9666666665) equal to 1.915144323 and -1.915144323.

Subproblem 1
x + 0.9666666665 = 1.915144323

Simplifying
x + 0.9666666665 = 1.915144323

Reorder the terms:
0.9666666665 + x = 1.915144323

Solving
0.9666666665 + x = 1.915144323

Solving for variable 'x'.

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

Add '-0.9666666665' to each side of the equation.
0.9666666665 + -0.9666666665 + x = 1.915144323 + -0.9666666665

Combine like terms: 0.9666666665 + -0.9666666665 = 0.0000000000
0.0000000000 + x = 1.915144323 + -0.9666666665
x = 1.915144323 + -0.9666666665

Combine like terms: 1.915144323 + -0.9666666665 = 0.9484776565
x = 0.9484776565

Simplifying
x = 0.9484776565

Subproblem 2
x + 0.9666666665 = -1.915144323

Simplifying
x + 0.9666666665 = -1.915144323

Reorder the terms:
0.9666666665 + x = -1.915144323

Solving
0.9666666665 + x = -1.915144323

Solving for variable 'x'.

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

Add '-0.9666666665' to each side of the equation.
0.9666666665 + -0.9666666665 + x = -1.915144323 + -0.9666666665

Combine like terms: 0.9666666665 + -0.9666666665 = 0.0000000000
0.0000000000 + x = -1.915144323 + -0.9666666665
x = -1.915144323 + -0.9666666665

Combine like terms: -1.915144323 + -0.9666666665 = -2.8818109895
x = -2.8818109895

Simplifying
x = -2.8818109895

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9484776565, -2.8818109895}
Solution
x = {0.9484776565, -2.8818109895}