4x(x-5)=11x-6

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

Simplifying
4x(x + -5) = 11x + -6

Reorder the terms:
4x(-5 + x) = 11x + -6
(-5 * 4x + x * 4x) = 11x + -6
(-20x + 4x2) = 11x + -6

Reorder the terms:
-20x + 4x2 = -6 + 11x

Solving
-20x + 4x2 = -6 + 11x

Solving for variable 'x'.

Reorder the terms:
6 + -20x + -11x + 4x2 = -6 + 11x + 6 + -11x

Combine like terms: -20x + -11x = -31x
6 + -31x + 4x2 = -6 + 11x + 6 + -11x

Reorder the terms:
6 + -31x + 4x2 = -6 + 6 + 11x + -11x

Combine like terms: -6 + 6 = 0
6 + -31x + 4x2 = 0 + 11x + -11x
6 + -31x + 4x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
6 + -31x + 4x2 = 0

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

Divide each side by '4'.
1.5 + -7.75x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -7.75x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -7.75x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -7.75x + x2 = 0 + -1.5
-7.75x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-7.75x + x2 = -1.5

The x term is -7.75x.  Take half its coefficient (-3.875).
Square it (15.015625) and add it to both sides.

Add '15.015625' to each side of the equation.
-7.75x + 15.015625 + x2 = -1.5 + 15.015625

Reorder the terms:
15.015625 + -7.75x + x2 = -1.5 + 15.015625

Combine like terms: -1.5 + 15.015625 = 13.515625
15.015625 + -7.75x + x2 = 13.515625

Factor a perfect square on the left side:
(x + -3.875)(x + -3.875) = 13.515625

Calculate the square root of the right side: 3.676360292

Break this problem into two subproblems by setting 
(x + -3.875) equal to 3.676360292 and -3.676360292.

Subproblem 1
x + -3.875 = 3.676360292

Simplifying
x + -3.875 = 3.676360292

Reorder the terms:
-3.875 + x = 3.676360292

Solving
-3.875 + x = 3.676360292

Solving for variable 'x'.

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

Add '3.875' to each side of the equation.
-3.875 + 3.875 + x = 3.676360292 + 3.875

Combine like terms: -3.875 + 3.875 = 0.000
0.000 + x = 3.676360292 + 3.875
x = 3.676360292 + 3.875

Combine like terms: 3.676360292 + 3.875 = 7.551360292
x = 7.551360292

Simplifying
x = 7.551360292

Subproblem 2
x + -3.875 = -3.676360292

Simplifying
x + -3.875 = -3.676360292

Reorder the terms:
-3.875 + x = -3.676360292

Solving
-3.875 + x = -3.676360292

Solving for variable 'x'.

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

Add '3.875' to each side of the equation.
-3.875 + 3.875 + x = -3.676360292 + 3.875

Combine like terms: -3.875 + 3.875 = 0.000
0.000 + x = -3.676360292 + 3.875
x = -3.676360292 + 3.875

Combine like terms: -3.676360292 + 3.875 = 0.198639708
x = 0.198639708

Simplifying
x = 0.198639708

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.551360292, 0.198639708}