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

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

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

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

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

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

Combine like terms: 3x + -1x = 2x
2(-3 + 2x + x2) = 84
(-3 * 2 + 2x * 2 + x2 * 2) = 84
(-6 + 4x + 2x2) = 84

Solving
-6 + 4x + 2x2 = 84

Solving for variable 'x'.

Reorder the terms:
-6 + -84 + 4x + 2x2 = 84 + -84

Combine like terms: -6 + -84 = -90
-90 + 4x + 2x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-90 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-45 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + 2x + x2 = 0

Solving
-45 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 2x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 2x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 2x + x2 = 0 + 45
2x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
2x + x2 = 45

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 = 45 + 1

Reorder the terms:
1 + 2x + x2 = 45 + 1

Combine like terms: 45 + 1 = 46
1 + 2x + x2 = 46

Factor a perfect square on the left side:
(x + 1)(x + 1) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 1) equal to 6.782329983 and -6.782329983.

Subproblem 1
x + 1 = 6.782329983

Simplifying
x + 1 = 6.782329983

Reorder the terms:
1 + x = 6.782329983

Solving
1 + x = 6.782329983

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 = 6.782329983 + -1

Combine like terms: 1 + -1 = 0
0 + x = 6.782329983 + -1
x = 6.782329983 + -1

Combine like terms: 6.782329983 + -1 = 5.782329983
x = 5.782329983

Simplifying
x = 5.782329983

Subproblem 2
x + 1 = -6.782329983

Simplifying
x + 1 = -6.782329983

Reorder the terms:
1 + x = -6.782329983

Solving
1 + x = -6.782329983

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 = -6.782329983 + -1

Combine like terms: 1 + -1 = 0
0 + x = -6.782329983 + -1
x = -6.782329983 + -1

Combine like terms: -6.782329983 + -1 = -7.782329983
x = -7.782329983

Simplifying
x = -7.782329983

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.782329983, -7.782329983}
Solution
x = {5.782329983, -7.782329983}