84=(x+6)(x-1)

Solution for 84=(x+6)(x-1) equation:

Simplifying
84 = (x + 6)(x + -1)

Reorder the terms:
84 = (6 + x)(x + -1)

Reorder the terms:
84 = (6 + x)(-1 + x)

Multiply (6 + x) * (-1 + x)
84 = (6(-1 + x) + x(-1 + x))
84 = ((-1 * 6 + x * 6) + x(-1 + x))
84 = ((-6 + 6x) + x(-1 + x))
84 = (-6 + 6x + (-1 * x + x * x))
84 = (-6 + 6x + (-1x + x2))

Combine like terms: 6x + -1x = 5x
84 = (-6 + 5x + x2)

Solving
84 = -6 + 5x + x2

Solving for variable 'x'.

Combine like terms: 84 + 6 = 90
90 + -5x + -1x2 = -6 + 5x + x2 + 6 + -5x + -1x2

Reorder the terms:
90 + -5x + -1x2 = -6 + 6 + 5x + -5x + x2 + -1x2

Combine like terms: -6 + 6 = 0
90 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2
90 + -5x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
90 + -5x + -1x2 = 0 + x2 + -1x2
90 + -5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
90 + -5x + -1x2 = 0

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

Divide each side by '-1'.
-90 + 5x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 5x + x2 = 0 + 90
5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
5x + x2 = 90

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 90 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 90 + 6.25

Combine like terms: 90 + 6.25 = 96.25
6.25 + 5x + x2 = 96.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.810708435 and -9.810708435.

Subproblem 1
x + 2.5 = 9.810708435

Simplifying
x + 2.5 = 9.810708435

Reorder the terms:
2.5 + x = 9.810708435

Solving
2.5 + x = 9.810708435

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 9.810708435 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.810708435 + -2.5
x = 9.810708435 + -2.5

Combine like terms: 9.810708435 + -2.5 = 7.310708435
x = 7.310708435

Simplifying
x = 7.310708435

Subproblem 2
x + 2.5 = -9.810708435

Simplifying
x + 2.5 = -9.810708435

Reorder the terms:
2.5 + x = -9.810708435

Solving
2.5 + x = -9.810708435

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -9.810708435 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.810708435 + -2.5
x = -9.810708435 + -2.5

Combine like terms: -9.810708435 + -2.5 = -12.310708435
x = -12.310708435

Simplifying
x = -12.310708435

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.310708435, -12.310708435}