(6x+20)(4x+10)=180

Solution for (6x+20)(4x+10)=180 equation:

Simplifying
(6x + 20)(4x + 10) = 180

Reorder the terms:
(20 + 6x)(4x + 10) = 180

Reorder the terms:
(20 + 6x)(10 + 4x) = 180

Multiply (20 + 6x) * (10 + 4x)
(20(10 + 4x) + 6x * (10 + 4x)) = 180
((10 * 20 + 4x * 20) + 6x * (10 + 4x)) = 180
((200 + 80x) + 6x * (10 + 4x)) = 180
(200 + 80x + (10 * 6x + 4x * 6x)) = 180
(200 + 80x + (60x + 24x2)) = 180

Combine like terms: 80x + 60x = 140x
(200 + 140x + 24x2) = 180

Solving
200 + 140x + 24x2 = 180

Solving for variable 'x'.

Reorder the terms:
200 + -180 + 140x + 24x2 = 180 + -180

Combine like terms: 200 + -180 = 20
20 + 140x + 24x2 = 180 + -180

Combine like terms: 180 + -180 = 0
20 + 140x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 35x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + 35x + 6x2)' equal to zero and attempt to solve:

Simplifying
5 + 35x + 6x2 = 0

Solving
5 + 35x + 6x2 = 0

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

Divide each side by '6'.
0.8333333333 + 5.833333333x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + 5.833333333x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + 5.833333333x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + 5.833333333x + x2 = 0 + -0.8333333333
5.833333333x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
5.833333333x + x2 = -0.8333333333

The x term is 5.833333333x.  Take half its coefficient (2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
5.833333333x + 8.506944446 + x2 = -0.8333333333 + 8.506944446

Reorder the terms:
8.506944446 + 5.833333333x + x2 = -0.8333333333 + 8.506944446

Combine like terms: -0.8333333333 + 8.506944446 = 7.6736111127
8.506944446 + 5.833333333x + x2 = 7.6736111127

Factor a perfect square on the left side:
(x + 2.916666667)(x + 2.916666667) = 7.6736111127

Calculate the square root of the right side: 2.770128357

Break this problem into two subproblems by setting 
(x + 2.916666667) equal to 2.770128357 and -2.770128357.

Subproblem 1
x + 2.916666667 = 2.770128357

Simplifying
x + 2.916666667 = 2.770128357

Reorder the terms:
2.916666667 + x = 2.770128357

Solving
2.916666667 + x = 2.770128357

Solving for variable 'x'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + x = 2.770128357 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + x = 2.770128357 + -2.916666667
x = 2.770128357 + -2.916666667

Combine like terms: 2.770128357 + -2.916666667 = -0.14653831
x = -0.14653831

Simplifying
x = -0.14653831

Subproblem 2
x + 2.916666667 = -2.770128357

Simplifying
x + 2.916666667 = -2.770128357

Reorder the terms:
2.916666667 + x = -2.770128357

Solving
2.916666667 + x = -2.770128357

Solving for variable 'x'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + x = -2.770128357 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + x = -2.770128357 + -2.916666667
x = -2.770128357 + -2.916666667

Combine like terms: -2.770128357 + -2.916666667 = -5.686795024
x = -5.686795024

Simplifying
x = -5.686795024

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.14653831, -5.686795024}
Solution
x = {-0.14653831, -5.686795024}