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

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

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

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

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

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

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

Solving
84 = -3 + 2x + x2

Solving for variable 'x'.

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

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

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

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

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-87 + 2x + x2 = 0

Move the constant term to the right:

Add '87' to each side of the equation.
-87 + 2x + 87 + x2 = 0 + 87

Reorder the terms:
-87 + 87 + 2x + x2 = 0 + 87

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

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

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 87 + 1

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

Combine like terms: 87 + 1 = 88
1 + 2x + x2 = 88

Factor a perfect square on the left side:
(x + 1)(x + 1) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(x + 1) equal to 9.38083152 and -9.38083152.

Subproblem 1
x + 1 = 9.38083152

Simplifying
x + 1 = 9.38083152

Reorder the terms:
1 + x = 9.38083152

Solving
1 + x = 9.38083152

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 9.38083152 + -1

Combine like terms: 1 + -1 = 0
0 + x = 9.38083152 + -1
x = 9.38083152 + -1

Combine like terms: 9.38083152 + -1 = 8.38083152
x = 8.38083152

Simplifying
x = 8.38083152

Subproblem 2
x + 1 = -9.38083152

Simplifying
x + 1 = -9.38083152

Reorder the terms:
1 + x = -9.38083152

Solving
1 + x = -9.38083152

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -9.38083152 + -1

Combine like terms: 1 + -1 = 0
0 + x = -9.38083152 + -1
x = -9.38083152 + -1

Combine like terms: -9.38083152 + -1 = -10.38083152
x = -10.38083152

Simplifying
x = -10.38083152

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.38083152, -10.38083152}