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

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

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

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

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

Multiply (3 + x) * (-2 + x)
2(3(-2 + x) + x(-2 + x)) = x(x + 3) + 84
2((-2 * 3 + x * 3) + x(-2 + x)) = x(x + 3) + 84
2((-6 + 3x) + x(-2 + x)) = x(x + 3) + 84
2(-6 + 3x + (-2 * x + x * x)) = x(x + 3) + 84
2(-6 + 3x + (-2x + x2)) = x(x + 3) + 84

Combine like terms: 3x + -2x = 1x
2(-6 + 1x + x2) = x(x + 3) + 84
(-6 * 2 + 1x * 2 + x2 * 2) = x(x + 3) + 84
(-12 + 2x + 2x2) = x(x + 3) + 84

Reorder the terms:
-12 + 2x + 2x2 = x(3 + x) + 84
-12 + 2x + 2x2 = (3 * x + x * x) + 84
-12 + 2x + 2x2 = (3x + x2) + 84

Reorder the terms:
-12 + 2x + 2x2 = 84 + 3x + x2

Solving
-12 + 2x + 2x2 = 84 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + -84 + 2x + -3x + 2x2 + -1x2 = 84 + 3x + x2 + -84 + -3x + -1x2

Combine like terms: -12 + -84 = -96
-96 + 2x + -3x + 2x2 + -1x2 = 84 + 3x + x2 + -84 + -3x + -1x2

Combine like terms: 2x + -3x = -1x
-96 + -1x + 2x2 + -1x2 = 84 + 3x + x2 + -84 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-96 + -1x + 1x2 = 84 + 3x + x2 + -84 + -3x + -1x2

Reorder the terms:
-96 + -1x + 1x2 = 84 + -84 + 3x + -3x + x2 + -1x2

Combine like terms: 84 + -84 = 0
-96 + -1x + 1x2 = 0 + 3x + -3x + x2 + -1x2
-96 + -1x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-96 + -1x + 1x2 = 0 + x2 + -1x2
-96 + -1x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-96 + -1x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '96' to each side of the equation.
-96 + -1x + 96 + x2 = 0 + 96

Reorder the terms:
-96 + 96 + -1x + x2 = 0 + 96

Combine like terms: -96 + 96 = 0
0 + -1x + x2 = 0 + 96
-1x + x2 = 0 + 96

Combine like terms: 0 + 96 = 96
-1x + x2 = 96

The x term is -1x.  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.
-1x + 0.25 + x2 = 96 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 96 + 0.25

Combine like terms: 96 + 0.25 = 96.25
0.25 + -1x + x2 = 96.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + -0.5) equal to 9.810708435 and -9.810708435.

Subproblem 1
x + -0.5 = 9.810708435

Simplifying
x + -0.5 = 9.810708435

Reorder the terms:
-0.5 + x = 9.810708435

Solving
-0.5 + x = 9.810708435

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 = 9.810708435 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 9.810708435 + 0.5
x = 9.810708435 + 0.5

Combine like terms: 9.810708435 + 0.5 = 10.310708435
x = 10.310708435

Simplifying
x = 10.310708435

Subproblem 2
x + -0.5 = -9.810708435

Simplifying
x + -0.5 = -9.810708435

Reorder the terms:
-0.5 + x = -9.810708435

Solving
-0.5 + x = -9.810708435

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 = -9.810708435 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -9.810708435 + 0.5
x = -9.810708435 + 0.5

Combine like terms: -9.810708435 + 0.5 = -9.310708435
x = -9.310708435

Simplifying
x = -9.310708435

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.310708435, -9.310708435}