(3x+2)*(2x+10)=90

Solution for (3x+2)*(2x+10)=90 equation:

Simplifying
(3x + 2)(2x + 10) = 90

Reorder the terms:
(2 + 3x)(2x + 10) = 90

Reorder the terms:
(2 + 3x)(10 + 2x) = 90

Multiply (2 + 3x) * (10 + 2x)
(2(10 + 2x) + 3x * (10 + 2x)) = 90
((10 * 2 + 2x * 2) + 3x * (10 + 2x)) = 90
((20 + 4x) + 3x * (10 + 2x)) = 90
(20 + 4x + (10 * 3x + 2x * 3x)) = 90
(20 + 4x + (30x + 6x2)) = 90

Combine like terms: 4x + 30x = 34x
(20 + 34x + 6x2) = 90

Solving
20 + 34x + 6x2 = 90

Solving for variable 'x'.

Reorder the terms:
20 + -90 + 34x + 6x2 = 90 + -90

Combine like terms: 20 + -90 = -70
-70 + 34x + 6x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-70 + 34x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 17x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-35 + 17x + 3x2)' equal to zero and attempt to solve:

Simplifying
-35 + 17x + 3x2 = 0

Solving
-35 + 17x + 3x2 = 0

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

Divide each side by '3'.
-11.66666667 + 5.666666667x + x2 = 0

Move the constant term to the right:

Add '11.66666667' to each side of the equation.
-11.66666667 + 5.666666667x + 11.66666667 + x2 = 0 + 11.66666667

Reorder the terms:
-11.66666667 + 11.66666667 + 5.666666667x + x2 = 0 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + 5.666666667x + x2 = 0 + 11.66666667
5.666666667x + x2 = 0 + 11.66666667

Combine like terms: 0 + 11.66666667 = 11.66666667
5.666666667x + x2 = 11.66666667

The x term is 5.666666667x.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667x + 8.027777782 + x2 = 11.66666667 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667x + x2 = 11.66666667 + 8.027777782

Combine like terms: 11.66666667 + 8.027777782 = 19.694444452
8.027777782 + 5.666666667x + x2 = 19.694444452

Factor a perfect square on the left side:
(x + 2.833333334)(x + 2.833333334) = 19.694444452

Calculate the square root of the right side: 4.437842319

Break this problem into two subproblems by setting 
(x + 2.833333334) equal to 4.437842319 and -4.437842319.

Subproblem 1
x + 2.833333334 = 4.437842319

Simplifying
x + 2.833333334 = 4.437842319

Reorder the terms:
2.833333334 + x = 4.437842319

Solving
2.833333334 + x = 4.437842319

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = 4.437842319 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = 4.437842319 + -2.833333334
x = 4.437842319 + -2.833333334

Combine like terms: 4.437842319 + -2.833333334 = 1.604508985
x = 1.604508985

Simplifying
x = 1.604508985

Subproblem 2
x + 2.833333334 = -4.437842319

Simplifying
x + 2.833333334 = -4.437842319

Reorder the terms:
2.833333334 + x = -4.437842319

Solving
2.833333334 + x = -4.437842319

Solving for variable 'x'.

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

Add '-2.833333334' to each side of the equation.
2.833333334 + -2.833333334 + x = -4.437842319 + -2.833333334

Combine like terms: 2.833333334 + -2.833333334 = 0.000000000
0.000000000 + x = -4.437842319 + -2.833333334
x = -4.437842319 + -2.833333334

Combine like terms: -4.437842319 + -2.833333334 = -7.271175653
x = -7.271175653

Simplifying
x = -7.271175653

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.604508985, -7.271175653}
Solution
x = {1.604508985, -7.271175653}