-3(x+10)2x=75

Solution for -3(x+10)2x=75 equation:

Simplifying
-3(x + 10) * 2x = 75

Reorder the terms:
-3(10 + x) * 2x = 75

Reorder the terms for easier multiplication:
-3 * 2x(10 + x) = 75

Multiply -3 * 2
-6x(10 + x) = 75
(10 * -6x + x * -6x) = 75
(-60x + -6x2) = 75

Solving
-60x + -6x2 = 75

Solving for variable 'x'.

Reorder the terms:
-75 + -60x + -6x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + -60x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(25 + 20x + 2x2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(25 + 20x + 2x2)' equal to zero and attempt to solve:

Simplifying
25 + 20x + 2x2 = 0

Solving
25 + 20x + 2x2 = 0

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

Divide each side by '2'.
12.5 + 10x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + 10x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + 10x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + 10x + x2 = 0 + -12.5
10x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
10x + x2 = -12.5

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 = -12.5 + 25

Reorder the terms:
25 + 10x + x2 = -12.5 + 25

Combine like terms: -12.5 + 25 = 12.5
25 + 10x + x2 = 12.5

Factor a perfect square on the left side:
(x + 5)(x + 5) = 12.5

Calculate the square root of the right side: 3.535533906

Break this problem into two subproblems by setting 
(x + 5) equal to 3.535533906 and -3.535533906.

Subproblem 1
x + 5 = 3.535533906

Simplifying
x + 5 = 3.535533906

Reorder the terms:
5 + x = 3.535533906

Solving
5 + x = 3.535533906

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 = 3.535533906 + -5

Combine like terms: 5 + -5 = 0
0 + x = 3.535533906 + -5
x = 3.535533906 + -5

Combine like terms: 3.535533906 + -5 = -1.464466094
x = -1.464466094

Simplifying
x = -1.464466094

Subproblem 2
x + 5 = -3.535533906

Simplifying
x + 5 = -3.535533906

Reorder the terms:
5 + x = -3.535533906

Solving
5 + x = -3.535533906

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 = -3.535533906 + -5

Combine like terms: 5 + -5 = 0
0 + x = -3.535533906 + -5
x = -3.535533906 + -5

Combine like terms: -3.535533906 + -5 = -8.535533906
x = -8.535533906

Simplifying
x = -8.535533906

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.464466094, -8.535533906}
Solution
x = {-1.464466094, -8.535533906}