-11(x+5)6x+4(x-4)=-45+35

Solution for -11(x+5)6x+4(x-4)=-45+35 equation:

Simplifying
-11(x + 5) * 6x + 4(x + -4) = -45 + 35

Reorder the terms:
-11(5 + x) * 6x + 4(x + -4) = -45 + 35

Reorder the terms for easier multiplication:
-11 * 6x(5 + x) + 4(x + -4) = -45 + 35

Multiply -11 * 6
-66x(5 + x) + 4(x + -4) = -45 + 35
(5 * -66x + x * -66x) + 4(x + -4) = -45 + 35
(-330x + -66x2) + 4(x + -4) = -45 + 35

Reorder the terms:
-330x + -66x2 + 4(-4 + x) = -45 + 35
-330x + -66x2 + (-4 * 4 + x * 4) = -45 + 35
-330x + -66x2 + (-16 + 4x) = -45 + 35

Reorder the terms:
-16 + -330x + 4x + -66x2 = -45 + 35

Combine like terms: -330x + 4x = -326x
-16 + -326x + -66x2 = -45 + 35

Combine like terms: -45 + 35 = -10
-16 + -326x + -66x2 = -10

Solving
-16 + -326x + -66x2 = -10

Solving for variable 'x'.

Reorder the terms:
-16 + 10 + -326x + -66x2 = -10 + 10

Combine like terms: -16 + 10 = -6
-6 + -326x + -66x2 = -10 + 10

Combine like terms: -10 + 10 = 0
-6 + -326x + -66x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 163x + 33x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 163x + 33x2)' equal to zero and attempt to solve:

Simplifying
3 + 163x + 33x2 = 0

Solving
3 + 163x + 33x2 = 0

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

Divide each side by '33'.
0.09090909091 + 4.939393939x + x2 = 0

Move the constant term to the right:

Add '-0.09090909091' to each side of the equation.
0.09090909091 + 4.939393939x + -0.09090909091 + x2 = 0 + -0.09090909091

Reorder the terms:
0.09090909091 + -0.09090909091 + 4.939393939x + x2 = 0 + -0.09090909091

Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000
0.00000000000 + 4.939393939x + x2 = 0 + -0.09090909091
4.939393939x + x2 = 0 + -0.09090909091

Combine like terms: 0 + -0.09090909091 = -0.09090909091
4.939393939x + x2 = -0.09090909091

The x term is 4.939393939x.  Take half its coefficient (2.46969697).
Square it (6.099403124) and add it to both sides.

Add '6.099403124' to each side of the equation.
4.939393939x + 6.099403124 + x2 = -0.09090909091 + 6.099403124

Reorder the terms:
6.099403124 + 4.939393939x + x2 = -0.09090909091 + 6.099403124

Combine like terms: -0.09090909091 + 6.099403124 = 6.00849403309
6.099403124 + 4.939393939x + x2 = 6.00849403309

Factor a perfect square on the left side:
(x + 2.46969697)(x + 2.46969697) = 6.00849403309

Calculate the square root of the right side: 2.451222967

Break this problem into two subproblems by setting 
(x + 2.46969697) equal to 2.451222967 and -2.451222967.

Subproblem 1
x + 2.46969697 = 2.451222967

Simplifying
x + 2.46969697 = 2.451222967

Reorder the terms:
2.46969697 + x = 2.451222967

Solving
2.46969697 + x = 2.451222967

Solving for variable 'x'.

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

Add '-2.46969697' to each side of the equation.
2.46969697 + -2.46969697 + x = 2.451222967 + -2.46969697

Combine like terms: 2.46969697 + -2.46969697 = 0.00000000
0.00000000 + x = 2.451222967 + -2.46969697
x = 2.451222967 + -2.46969697

Combine like terms: 2.451222967 + -2.46969697 = -0.018474003
x = -0.018474003

Simplifying
x = -0.018474003

Subproblem 2
x + 2.46969697 = -2.451222967

Simplifying
x + 2.46969697 = -2.451222967

Reorder the terms:
2.46969697 + x = -2.451222967

Solving
2.46969697 + x = -2.451222967

Solving for variable 'x'.

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

Add '-2.46969697' to each side of the equation.
2.46969697 + -2.46969697 + x = -2.451222967 + -2.46969697

Combine like terms: 2.46969697 + -2.46969697 = 0.00000000
0.00000000 + x = -2.451222967 + -2.46969697
x = -2.451222967 + -2.46969697

Combine like terms: -2.451222967 + -2.46969697 = -4.920919937
x = -4.920919937

Simplifying
x = -4.920919937

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.018474003, -4.920919937}
Solution
x = {-0.018474003, -4.920919937}