(3x+7)6x+-20=90

Solution for (3x+7)6x+-20=90 equation:

Simplifying
(3x + 7) * 6x + -20 = 90

Reorder the terms:
(7 + 3x) * 6x + -20 = 90

Reorder the terms for easier multiplication:
6x(7 + 3x) + -20 = 90
(7 * 6x + 3x * 6x) + -20 = 90
(42x + 18x2) + -20 = 90

Reorder the terms:
-20 + 42x + 18x2 = 90

Solving
-20 + 42x + 18x2 = 90

Solving for variable 'x'.

Reorder the terms:
-20 + -90 + 42x + 18x2 = 90 + -90

Combine like terms: -20 + -90 = -110
-110 + 42x + 18x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-110 + 42x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + 21x + 9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-55 + 21x + 9x2)' equal to zero and attempt to solve:

Simplifying
-55 + 21x + 9x2 = 0

Solving
-55 + 21x + 9x2 = 0

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

Divide each side by '9'.
-6.111111111 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '6.111111111' to each side of the equation.
-6.111111111 + 2.333333333x + 6.111111111 + x2 = 0 + 6.111111111

Reorder the terms:
-6.111111111 + 6.111111111 + 2.333333333x + x2 = 0 + 6.111111111

Combine like terms: -6.111111111 + 6.111111111 = 0.000000000
0.000000000 + 2.333333333x + x2 = 0 + 6.111111111
2.333333333x + x2 = 0 + 6.111111111

Combine like terms: 0 + 6.111111111 = 6.111111111
2.333333333x + x2 = 6.111111111

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 6.111111111 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 6.111111111 + 1.361111112

Combine like terms: 6.111111111 + 1.361111112 = 7.472222223
1.361111112 + 2.333333333x + x2 = 7.472222223

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 7.472222223

Calculate the square root of the right side: 2.733536578

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 2.733536578 and -2.733536578.

Subproblem 1
x + 1.166666667 = 2.733536578

Simplifying
x + 1.166666667 = 2.733536578

Reorder the terms:
1.166666667 + x = 2.733536578

Solving
1.166666667 + x = 2.733536578

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 2.733536578 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 2.733536578 + -1.166666667
x = 2.733536578 + -1.166666667

Combine like terms: 2.733536578 + -1.166666667 = 1.566869911
x = 1.566869911

Simplifying
x = 1.566869911

Subproblem 2
x + 1.166666667 = -2.733536578

Simplifying
x + 1.166666667 = -2.733536578

Reorder the terms:
1.166666667 + x = -2.733536578

Solving
1.166666667 + x = -2.733536578

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -2.733536578 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -2.733536578 + -1.166666667
x = -2.733536578 + -1.166666667

Combine like terms: -2.733536578 + -1.166666667 = -3.900203245
x = -3.900203245

Simplifying
x = -3.900203245

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.566869911, -3.900203245}
Solution
x = {1.566869911, -3.900203245}