x(4x-11)=(x+1)(x-3)

Solution for x(4x-11)=(x+1)(x-3) equation:

Simplifying
x(4x + -11) = (x + 1)(x + -3)

Reorder the terms:
x(-11 + 4x) = (x + 1)(x + -3)
(-11 * x + 4x * x) = (x + 1)(x + -3)
(-11x + 4x2) = (x + 1)(x + -3)

Reorder the terms:
-11x + 4x2 = (1 + x)(x + -3)

Reorder the terms:
-11x + 4x2 = (1 + x)(-3 + x)

Multiply (1 + x) * (-3 + x)
-11x + 4x2 = (1(-3 + x) + x(-3 + x))
-11x + 4x2 = ((-3 * 1 + x * 1) + x(-3 + x))
-11x + 4x2 = ((-3 + 1x) + x(-3 + x))
-11x + 4x2 = (-3 + 1x + (-3 * x + x * x))
-11x + 4x2 = (-3 + 1x + (-3x + x2))

Combine like terms: 1x + -3x = -2x
-11x + 4x2 = (-3 + -2x + x2)

Solving
-11x + 4x2 = -3 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
3 + -11x + 2x + 4x2 + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2

Combine like terms: -11x + 2x = -9x
3 + -9x + 4x2 + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
3 + -9x + 3x2 = -3 + -2x + x2 + 3 + 2x + -1x2

Reorder the terms:
3 + -9x + 3x2 = -3 + 3 + -2x + 2x + x2 + -1x2

Combine like terms: -3 + 3 = 0
3 + -9x + 3x2 = 0 + -2x + 2x + x2 + -1x2
3 + -9x + 3x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
3 + -9x + 3x2 = 0 + x2 + -1x2
3 + -9x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -3x + x2) = 0

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

Simplifying
1 + -3x + x2 = 0

Solving
1 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -3x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x + x2 = 0 + -1
-3x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3x + x2 = -1

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3x + x2 = 1.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + -1.5 = 1.118033989

Simplifying
x + -1.5 = 1.118033989

Reorder the terms:
-1.5 + x = 1.118033989

Solving
-1.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.118033989 + 1.5
x = 1.118033989 + 1.5

Combine like terms: 1.118033989 + 1.5 = 2.618033989
x = 2.618033989

Simplifying
x = 2.618033989

Subproblem 2
x + -1.5 = -1.118033989

Simplifying
x + -1.5 = -1.118033989

Reorder the terms:
-1.5 + x = -1.118033989

Solving
-1.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.118033989 + 1.5
x = -1.118033989 + 1.5

Combine like terms: -1.118033989 + 1.5 = 0.381966011
x = 0.381966011

Simplifying
x = 0.381966011

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.618033989, 0.381966011}
Solution
x = {2.618033989, 0.381966011}