2(x+9)(x-4)=(x+7)x+84

Solution for 2(x+9)(x-4)=(x+7)x+84 equation:

Simplifying
2(x + 9)(x + -4) = (x + 7) * x + 84

Reorder the terms:
2(9 + x)(x + -4) = (x + 7) * x + 84

Reorder the terms:
2(9 + x)(-4 + x) = (x + 7) * x + 84

Multiply (9 + x) * (-4 + x)
2(9(-4 + x) + x(-4 + x)) = (x + 7) * x + 84
2((-4 * 9 + x * 9) + x(-4 + x)) = (x + 7) * x + 84
2((-36 + 9x) + x(-4 + x)) = (x + 7) * x + 84
2(-36 + 9x + (-4 * x + x * x)) = (x + 7) * x + 84
2(-36 + 9x + (-4x + x2)) = (x + 7) * x + 84

Combine like terms: 9x + -4x = 5x
2(-36 + 5x + x2) = (x + 7) * x + 84
(-36 * 2 + 5x * 2 + x2 * 2) = (x + 7) * x + 84
(-72 + 10x + 2x2) = (x + 7) * x + 84

Reorder the terms:
-72 + 10x + 2x2 = (7 + x) * x + 84

Reorder the terms for easier multiplication:
-72 + 10x + 2x2 = x(7 + x) + 84
-72 + 10x + 2x2 = (7 * x + x * x) + 84
-72 + 10x + 2x2 = (7x + x2) + 84

Reorder the terms:
-72 + 10x + 2x2 = 84 + 7x + x2

Solving
-72 + 10x + 2x2 = 84 + 7x + x2

Solving for variable 'x'.

Reorder the terms:
-72 + -84 + 10x + -7x + 2x2 + -1x2 = 84 + 7x + x2 + -84 + -7x + -1x2

Combine like terms: -72 + -84 = -156
-156 + 10x + -7x + 2x2 + -1x2 = 84 + 7x + x2 + -84 + -7x + -1x2

Combine like terms: 10x + -7x = 3x
-156 + 3x + 2x2 + -1x2 = 84 + 7x + x2 + -84 + -7x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-156 + 3x + 1x2 = 84 + 7x + x2 + -84 + -7x + -1x2

Reorder the terms:
-156 + 3x + 1x2 = 84 + -84 + 7x + -7x + x2 + -1x2

Combine like terms: 84 + -84 = 0
-156 + 3x + 1x2 = 0 + 7x + -7x + x2 + -1x2
-156 + 3x + 1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-156 + 3x + 1x2 = 0 + x2 + -1x2
-156 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-156 + 3x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '156' to each side of the equation.
-156 + 3x + 156 + x2 = 0 + 156

Reorder the terms:
-156 + 156 + 3x + x2 = 0 + 156

Combine like terms: -156 + 156 = 0
0 + 3x + x2 = 0 + 156
3x + x2 = 0 + 156

Combine like terms: 0 + 156 = 156
3x + x2 = 156

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 156 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 156 + 2.25

Combine like terms: 156 + 2.25 = 158.25
2.25 + 3x + x2 = 158.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 158.25

Calculate the square root of the right side: 12.579745625

Break this problem into two subproblems by setting 
(x + 1.5) equal to 12.579745625 and -12.579745625.

Subproblem 1
x + 1.5 = 12.579745625

Simplifying
x + 1.5 = 12.579745625

Reorder the terms:
1.5 + x = 12.579745625

Solving
1.5 + x = 12.579745625

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 12.579745625 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 12.579745625 + -1.5
x = 12.579745625 + -1.5

Combine like terms: 12.579745625 + -1.5 = 11.079745625
x = 11.079745625

Simplifying
x = 11.079745625

Subproblem 2
x + 1.5 = -12.579745625

Simplifying
x + 1.5 = -12.579745625

Reorder the terms:
1.5 + x = -12.579745625

Solving
1.5 + x = -12.579745625

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -12.579745625 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -12.579745625 + -1.5
x = -12.579745625 + -1.5

Combine like terms: -12.579745625 + -1.5 = -14.079745625
x = -14.079745625

Simplifying
x = -14.079745625

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.079745625, -14.079745625}