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

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

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

Reorder the terms:
6x(-5 + x) + 9 = 3(x + -4)
(-5 * 6x + x * 6x) + 9 = 3(x + -4)
(-30x + 6x2) + 9 = 3(x + -4)

Reorder the terms:
9 + -30x + 6x2 = 3(x + -4)

Reorder the terms:
9 + -30x + 6x2 = 3(-4 + x)
9 + -30x + 6x2 = (-4 * 3 + x * 3)
9 + -30x + 6x2 = (-12 + 3x)

Solving
9 + -30x + 6x2 = -12 + 3x

Solving for variable 'x'.

Reorder the terms:
9 + 12 + -30x + -3x + 6x2 = -12 + 3x + 12 + -3x

Combine like terms: 9 + 12 = 21
21 + -30x + -3x + 6x2 = -12 + 3x + 12 + -3x

Combine like terms: -30x + -3x = -33x
21 + -33x + 6x2 = -12 + 3x + 12 + -3x

Reorder the terms:
21 + -33x + 6x2 = -12 + 12 + 3x + -3x

Combine like terms: -12 + 12 = 0
21 + -33x + 6x2 = 0 + 3x + -3x
21 + -33x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
21 + -33x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -11x + 2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + -11x + 2x2)' equal to zero and attempt to solve:

Simplifying
7 + -11x + 2x2 = 0

Solving
7 + -11x + 2x2 = 0

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

Divide each side by '2'.
3.5 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -5.5x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -5.5x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -5.5x + x2 = 0 + -3.5
-5.5x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-5.5x + x2 = -3.5

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -3.5 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -3.5 + 7.5625

Combine like terms: -3.5 + 7.5625 = 4.0625
7.5625 + -5.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + -2.75) equal to 2.015564437 and -2.015564437.

Subproblem 1
x + -2.75 = 2.015564437

Simplifying
x + -2.75 = 2.015564437

Reorder the terms:
-2.75 + x = 2.015564437

Solving
-2.75 + x = 2.015564437

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 2.015564437 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 2.015564437 + 2.75
x = 2.015564437 + 2.75

Combine like terms: 2.015564437 + 2.75 = 4.765564437
x = 4.765564437

Simplifying
x = 4.765564437

Subproblem 2
x + -2.75 = -2.015564437

Simplifying
x + -2.75 = -2.015564437

Reorder the terms:
-2.75 + x = -2.015564437

Solving
-2.75 + x = -2.015564437

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -2.015564437 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -2.015564437 + 2.75
x = -2.015564437 + 2.75

Combine like terms: -2.015564437 + 2.75 = 0.734435563
x = 0.734435563

Simplifying
x = 0.734435563

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.765564437, 0.734435563}
Solution
x = {4.765564437, 0.734435563}