84=(2x+3)(x-1)

Solution for 84=(2x+3)(x-1) equation:

Simplifying
84 = (2x + 3)(x + -1)

Reorder the terms:
84 = (3 + 2x)(x + -1)

Reorder the terms:
84 = (3 + 2x)(-1 + x)

Multiply (3 + 2x) * (-1 + x)
84 = (3(-1 + x) + 2x * (-1 + x))
84 = ((-1 * 3 + x * 3) + 2x * (-1 + x))
84 = ((-3 + 3x) + 2x * (-1 + x))
84 = (-3 + 3x + (-1 * 2x + x * 2x))
84 = (-3 + 3x + (-2x + 2x2))

Combine like terms: 3x + -2x = 1x
84 = (-3 + 1x + 2x2)

Solving
84 = -3 + 1x + 2x2

Solving for variable 'x'.

Combine like terms: 84 + 3 = 87
87 + -1x + -2x2 = -3 + 1x + 2x2 + 3 + -1x + -2x2

Reorder the terms:
87 + -1x + -2x2 = -3 + 3 + 1x + -1x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
87 + -1x + -2x2 = 0 + 1x + -1x + 2x2 + -2x2
87 + -1x + -2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
87 + -1x + -2x2 = 0 + 2x2 + -2x2
87 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
87 + -1x + -2x2 = 0

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

Divide each side by '-2'.
-43.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '43.5' to each side of the equation.
-43.5 + 0.5x + 43.5 + x2 = 0 + 43.5

Reorder the terms:
-43.5 + 43.5 + 0.5x + x2 = 0 + 43.5

Combine like terms: -43.5 + 43.5 = 0.0
0.0 + 0.5x + x2 = 0 + 43.5
0.5x + x2 = 0 + 43.5

Combine like terms: 0 + 43.5 = 43.5
0.5x + x2 = 43.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 43.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 43.5 + 0.0625

Combine like terms: 43.5 + 0.0625 = 43.5625
0.0625 + 0.5x + x2 = 43.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 43.5625

Calculate the square root of the right side: 6.600189391

Break this problem into two subproblems by setting 
(x + 0.25) equal to 6.600189391 and -6.600189391.

Subproblem 1
x + 0.25 = 6.600189391

Simplifying
x + 0.25 = 6.600189391

Reorder the terms:
0.25 + x = 6.600189391

Solving
0.25 + x = 6.600189391

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 6.600189391 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 6.600189391 + -0.25
x = 6.600189391 + -0.25

Combine like terms: 6.600189391 + -0.25 = 6.350189391
x = 6.350189391

Simplifying
x = 6.350189391

Subproblem 2
x + 0.25 = -6.600189391

Simplifying
x + 0.25 = -6.600189391

Reorder the terms:
0.25 + x = -6.600189391

Solving
0.25 + x = -6.600189391

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -6.600189391 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -6.600189391 + -0.25
x = -6.600189391 + -0.25

Combine like terms: -6.600189391 + -0.25 = -6.850189391
x = -6.850189391

Simplifying
x = -6.850189391

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.350189391, -6.850189391}