2(x-10)3x-10=90

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

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

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

Reorder the terms for easier multiplication:
2 * 3x(-10 + x) + -10 = 90

Multiply 2 * 3
6x(-10 + x) + -10 = 90
(-10 * 6x + x * 6x) + -10 = 90
(-60x + 6x2) + -10 = 90

Reorder the terms:
-10 + -60x + 6x2 = 90

Solving
-10 + -60x + 6x2 = 90

Solving for variable 'x'.

Reorder the terms:
-10 + -90 + -60x + 6x2 = 90 + -90

Combine like terms: -10 + -90 = -100
-100 + -60x + 6x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-100 + -60x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -30x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + -30x + 3x2)' equal to zero and attempt to solve:

Simplifying
-50 + -30x + 3x2 = 0

Solving
-50 + -30x + 3x2 = 0

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

Divide each side by '3'.
-16.66666667 + -10x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -10x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -10x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -10x + x2 = 0 + 16.66666667
-10x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-10x + x2 = 16.66666667

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 16.66666667 + 25

Reorder the terms:
25 + -10x + x2 = 16.66666667 + 25

Combine like terms: 16.66666667 + 25 = 41.66666667
25 + -10x + x2 = 41.66666667

Factor a perfect square on the left side:
(x + -5)(x + -5) = 41.66666667

Calculate the square root of the right side: 6.454972244

Break this problem into two subproblems by setting 
(x + -5) equal to 6.454972244 and -6.454972244.

Subproblem 1
x + -5 = 6.454972244

Simplifying
x + -5 = 6.454972244

Reorder the terms:
-5 + x = 6.454972244

Solving
-5 + x = 6.454972244

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 6.454972244 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.454972244 + 5
x = 6.454972244 + 5

Combine like terms: 6.454972244 + 5 = 11.454972244
x = 11.454972244

Simplifying
x = 11.454972244

Subproblem 2
x + -5 = -6.454972244

Simplifying
x + -5 = -6.454972244

Reorder the terms:
-5 + x = -6.454972244

Solving
-5 + x = -6.454972244

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -6.454972244 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.454972244 + 5
x = -6.454972244 + 5

Combine like terms: -6.454972244 + 5 = -1.454972244
x = -1.454972244

Simplifying
x = -1.454972244

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.454972244, -1.454972244}
Solution
x = {11.454972244, -1.454972244}