3(4x-7)-2x(x-9)=37

Solution for 3(4x-7)-2x(x-9)=37 equation:

Simplifying
3(4x + -7) + -2x(x + -9) = 37

Reorder the terms:
3(-7 + 4x) + -2x(x + -9) = 37
(-7 * 3 + 4x * 3) + -2x(x + -9) = 37
(-21 + 12x) + -2x(x + -9) = 37

Reorder the terms:
-21 + 12x + -2x(-9 + x) = 37
-21 + 12x + (-9 * -2x + x * -2x) = 37
-21 + 12x + (18x + -2x2) = 37

Combine like terms: 12x + 18x = 30x
-21 + 30x + -2x2 = 37

Solving
-21 + 30x + -2x2 = 37

Solving for variable 'x'.

Reorder the terms:
-21 + -37 + 30x + -2x2 = 37 + -37

Combine like terms: -21 + -37 = -58
-58 + 30x + -2x2 = 37 + -37

Combine like terms: 37 + -37 = 0
-58 + 30x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-29 + 15x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-29 + 15x + -1x2)' equal to zero and attempt to solve:

Simplifying
-29 + 15x + -1x2 = 0

Solving
-29 + 15x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
29 + -15x + x2 = 0

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + -15x + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + -15x + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -15x + x2 = 0 + -29
-15x + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
-15x + x2 = -29

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -29 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -29 + 56.25

Combine like terms: -29 + 56.25 = 27.25
56.25 + -15x + x2 = 27.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -7.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
x + -7.5 = 5.220153254

Simplifying
x + -7.5 = 5.220153254

Reorder the terms:
-7.5 + x = 5.220153254

Solving
-7.5 + x = 5.220153254

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 5.220153254 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 5.220153254 + 7.5
x = 5.220153254 + 7.5

Combine like terms: 5.220153254 + 7.5 = 12.720153254
x = 12.720153254

Simplifying
x = 12.720153254

Subproblem 2
x + -7.5 = -5.220153254

Simplifying
x + -7.5 = -5.220153254

Reorder the terms:
-7.5 + x = -5.220153254

Solving
-7.5 + x = -5.220153254

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -5.220153254 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -5.220153254 + 7.5
x = -5.220153254 + 7.5

Combine like terms: -5.220153254 + 7.5 = 2.279846746
x = 2.279846746

Simplifying
x = 2.279846746

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.720153254, 2.279846746}
Solution
x = {12.720153254, 2.279846746}