37x(x-2+5)(35x-45)=6x

Solution for 37x(x-2+5)(35x-45)=6x equation:

Simplifying
37x(x + -2 + 5)(35x + -45) = 6x

Reorder the terms:
37x(-2 + 5 + x)(35x + -45) = 6x

Combine like terms: -2 + 5 = 3
37x(3 + x)(35x + -45) = 6x

Reorder the terms:
37x(3 + x)(-45 + 35x) = 6x

Multiply (3 + x) * (-45 + 35x)
37x(3(-45 + 35x) + x(-45 + 35x)) = 6x
37x((-45 * 3 + 35x * 3) + x(-45 + 35x)) = 6x
37x((-135 + 105x) + x(-45 + 35x)) = 6x
37x(-135 + 105x + (-45 * x + 35x * x)) = 6x
37x(-135 + 105x + (-45x + 35x2)) = 6x

Combine like terms: 105x + -45x = 60x
37x(-135 + 60x + 35x2) = 6x
(-135 * 37x + 60x * 37x + 35x2 * 37x) = 6x
(-4995x + 2220x2 + 1295x3) = 6x

Solving
-4995x + 2220x2 + 1295x3 = 6x

Solving for variable 'x'.

Reorder the terms:
-4995x + -6x + 2220x2 + 1295x3 = 6x + -6x

Combine like terms: -4995x + -6x = -5001x
-5001x + 2220x2 + 1295x3 = 6x + -6x

Combine like terms: 6x + -6x = 0
-5001x + 2220x2 + 1295x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5001 + 2220x + 1295x2) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-5001 + 2220x + 1295x2)' equal to zero and attempt to solve:

Simplifying
-5001 + 2220x + 1295x2 = 0

Solving
-5001 + 2220x + 1295x2 = 0

Begin completing the square.  Divide all terms by
1295 the coefficient of the squared term: 

Divide each side by '1295'.
-3.861776062 + 1.714285714x + x2 = 0

Move the constant term to the right:

Add '3.861776062' to each side of the equation.
-3.861776062 + 1.714285714x + 3.861776062 + x2 = 0 + 3.861776062

Reorder the terms:
-3.861776062 + 3.861776062 + 1.714285714x + x2 = 0 + 3.861776062

Combine like terms: -3.861776062 + 3.861776062 = 0.000000000
0.000000000 + 1.714285714x + x2 = 0 + 3.861776062
1.714285714x + x2 = 0 + 3.861776062

Combine like terms: 0 + 3.861776062 = 3.861776062
1.714285714x + x2 = 3.861776062

The x term is 1.714285714x.  Take half its coefficient (0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
1.714285714x + 0.7346938773 + x2 = 3.861776062 + 0.7346938773

Reorder the terms:
0.7346938773 + 1.714285714x + x2 = 3.861776062 + 0.7346938773

Combine like terms: 3.861776062 + 0.7346938773 = 4.5964699393
0.7346938773 + 1.714285714x + x2 = 4.5964699393

Factor a perfect square on the left side:
(x + 0.857142857)(x + 0.857142857) = 4.5964699393

Calculate the square root of the right side: 2.143937951

Break this problem into two subproblems by setting 
(x + 0.857142857) equal to 2.143937951 and -2.143937951.

Subproblem 1
x + 0.857142857 = 2.143937951

Simplifying
x + 0.857142857 = 2.143937951

Reorder the terms:
0.857142857 + x = 2.143937951

Solving
0.857142857 + x = 2.143937951

Solving for variable 'x'.

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

Add '-0.857142857' to each side of the equation.
0.857142857 + -0.857142857 + x = 2.143937951 + -0.857142857

Combine like terms: 0.857142857 + -0.857142857 = 0.000000000
0.000000000 + x = 2.143937951 + -0.857142857
x = 2.143937951 + -0.857142857

Combine like terms: 2.143937951 + -0.857142857 = 1.286795094
x = 1.286795094

Simplifying
x = 1.286795094

Subproblem 2
x + 0.857142857 = -2.143937951

Simplifying
x + 0.857142857 = -2.143937951

Reorder the terms:
0.857142857 + x = -2.143937951

Solving
0.857142857 + x = -2.143937951

Solving for variable 'x'.

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

Add '-0.857142857' to each side of the equation.
0.857142857 + -0.857142857 + x = -2.143937951 + -0.857142857

Combine like terms: 0.857142857 + -0.857142857 = 0.000000000
0.000000000 + x = -2.143937951 + -0.857142857
x = -2.143937951 + -0.857142857

Combine like terms: -2.143937951 + -0.857142857 = -3.001080808
x = -3.001080808

Simplifying
x = -3.001080808

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.286795094, -3.001080808}
Solution
x = {0, 1.286795094, -3.001080808}