5x(2x-9)+6x=3(2x-4)+7

Solution for 5x(2x-9)+6x=3(2x-4)+7 equation:

Simplifying
5x(2x + -9) + 6x = 3(2x + -4) + 7

Reorder the terms:
5x(-9 + 2x) + 6x = 3(2x + -4) + 7
(-9 * 5x + 2x * 5x) + 6x = 3(2x + -4) + 7
(-45x + 10x2) + 6x = 3(2x + -4) + 7

Reorder the terms:
-45x + 6x + 10x2 = 3(2x + -4) + 7

Combine like terms: -45x + 6x = -39x
-39x + 10x2 = 3(2x + -4) + 7

Reorder the terms:
-39x + 10x2 = 3(-4 + 2x) + 7
-39x + 10x2 = (-4 * 3 + 2x * 3) + 7
-39x + 10x2 = (-12 + 6x) + 7

Reorder the terms:
-39x + 10x2 = -12 + 7 + 6x

Combine like terms: -12 + 7 = -5
-39x + 10x2 = -5 + 6x

Solving
-39x + 10x2 = -5 + 6x

Solving for variable 'x'.

Reorder the terms:
5 + -39x + -6x + 10x2 = -5 + 6x + 5 + -6x

Combine like terms: -39x + -6x = -45x
5 + -45x + 10x2 = -5 + 6x + 5 + -6x

Reorder the terms:
5 + -45x + 10x2 = -5 + 5 + 6x + -6x

Combine like terms: -5 + 5 = 0
5 + -45x + 10x2 = 0 + 6x + -6x
5 + -45x + 10x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
5 + -45x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -9x + 2x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + -9x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + -9x + 2x2 = 0

Solving
1 + -9x + 2x2 = 0

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

Divide each side by '2'.
0.5 + -4.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -4.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -4.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -4.5x + x2 = 0 + -0.5
-4.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-4.5x + x2 = -0.5

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = -0.5 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -0.5 + 5.0625

Combine like terms: -0.5 + 5.0625 = 4.5625
5.0625 + -4.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
x + -2.25 = 2.136000936

Simplifying
x + -2.25 = 2.136000936

Reorder the terms:
-2.25 + x = 2.136000936

Solving
-2.25 + x = 2.136000936

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.136000936 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.136000936 + 2.25
x = 2.136000936 + 2.25

Combine like terms: 2.136000936 + 2.25 = 4.386000936
x = 4.386000936

Simplifying
x = 4.386000936

Subproblem 2
x + -2.25 = -2.136000936

Simplifying
x + -2.25 = -2.136000936

Reorder the terms:
-2.25 + x = -2.136000936

Solving
-2.25 + x = -2.136000936

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.136000936 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.136000936 + 2.25
x = -2.136000936 + 2.25

Combine like terms: -2.136000936 + 2.25 = 0.113999064
x = 0.113999064

Simplifying
x = 0.113999064

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.386000936, 0.113999064}
Solution
x = {4.386000936, 0.113999064}