133=(2x+1)(x-1)

Solution for 133=(2x+1)(x-1) equation:

Simplifying
133 = (2x + 1)(x + -1)

Reorder the terms:
133 = (1 + 2x)(x + -1)

Reorder the terms:
133 = (1 + 2x)(-1 + x)

Multiply (1 + 2x) * (-1 + x)
133 = (1(-1 + x) + 2x * (-1 + x))
133 = ((-1 * 1 + x * 1) + 2x * (-1 + x))
133 = ((-1 + 1x) + 2x * (-1 + x))
133 = (-1 + 1x + (-1 * 2x + x * 2x))
133 = (-1 + 1x + (-2x + 2x2))

Combine like terms: 1x + -2x = -1x
133 = (-1 + -1x + 2x2)

Solving
133 = -1 + -1x + 2x2

Solving for variable 'x'.

Combine like terms: 133 + 1 = 134
134 + x + -2x2 = -1 + -1x + 2x2 + 1 + x + -2x2

Reorder the terms:
134 + x + -2x2 = -1 + 1 + -1x + x + 2x2 + -2x2

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

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

Combine like terms: 2x2 + -2x2 = 0
134 + x + -2x2 = 0

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

Divide each side by '-2'.
-67 + -0.5x + x2 = 0

Move the constant term to the right:

Add '67' to each side of the equation.
-67 + -0.5x + 67 + x2 = 0 + 67

Reorder the terms:
-67 + 67 + -0.5x + x2 = 0 + 67

Combine like terms: -67 + 67 = 0
0 + -0.5x + x2 = 0 + 67
-0.5x + x2 = 0 + 67

Combine like terms: 0 + 67 = 67
-0.5x + x2 = 67

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.5x + 0.25 + x2 = 67 + 0.25

Reorder the terms:
0.25 + -0.5x + x2 = 67 + 0.25

Combine like terms: 67 + 0.25 = 67.25
0.25 + -0.5x + x2 = 67.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 67.25

Calculate the square root of the right side: 8.200609733

Break this problem into two subproblems by setting 
(x + 0.5) equal to 8.200609733 and -8.200609733.

Subproblem 1
x + 0.5 = 8.200609733

Simplifying
x + 0.5 = 8.200609733

Reorder the terms:
0.5 + x = 8.200609733

Solving
0.5 + x = 8.200609733

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 8.200609733 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 8.200609733 + -0.5
x = 8.200609733 + -0.5

Combine like terms: 8.200609733 + -0.5 = 7.700609733
x = 7.700609733

Simplifying
x = 7.700609733

Subproblem 2
x + 0.5 = -8.200609733

Simplifying
x + 0.5 = -8.200609733

Reorder the terms:
0.5 + x = -8.200609733

Solving
0.5 + x = -8.200609733

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -8.200609733 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -8.200609733 + -0.5
x = -8.200609733 + -0.5

Combine like terms: -8.200609733 + -0.5 = -8.700609733
x = -8.700609733

Simplifying
x = -8.700609733

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.700609733, -8.700609733}