2(x+9)(x-4)=(x-9)x+60

Solution for 2(x+9)(x-4)=(x-9)x+60 equation:

Simplifying
2(x + 9)(x + -4) = (x + -9) * x + 60

Reorder the terms:
2(9 + x)(x + -4) = (x + -9) * x + 60

Reorder the terms:
2(9 + x)(-4 + x) = (x + -9) * x + 60

Multiply (9 + x) * (-4 + x)
2(9(-4 + x) + x(-4 + x)) = (x + -9) * x + 60
2((-4 * 9 + x * 9) + x(-4 + x)) = (x + -9) * x + 60
2((-36 + 9x) + x(-4 + x)) = (x + -9) * x + 60
2(-36 + 9x + (-4 * x + x * x)) = (x + -9) * x + 60
2(-36 + 9x + (-4x + x2)) = (x + -9) * x + 60

Combine like terms: 9x + -4x = 5x
2(-36 + 5x + x2) = (x + -9) * x + 60
(-36 * 2 + 5x * 2 + x2 * 2) = (x + -9) * x + 60
(-72 + 10x + 2x2) = (x + -9) * x + 60

Reorder the terms:
-72 + 10x + 2x2 = (-9 + x) * x + 60

Reorder the terms for easier multiplication:
-72 + 10x + 2x2 = x(-9 + x) + 60
-72 + 10x + 2x2 = (-9 * x + x * x) + 60
-72 + 10x + 2x2 = (-9x + x2) + 60

Reorder the terms:
-72 + 10x + 2x2 = 60 + -9x + x2

Solving
-72 + 10x + 2x2 = 60 + -9x + x2

Solving for variable 'x'.

Reorder the terms:
-72 + -60 + 10x + 9x + 2x2 + -1x2 = 60 + -9x + x2 + -60 + 9x + -1x2

Combine like terms: -72 + -60 = -132
-132 + 10x + 9x + 2x2 + -1x2 = 60 + -9x + x2 + -60 + 9x + -1x2

Combine like terms: 10x + 9x = 19x
-132 + 19x + 2x2 + -1x2 = 60 + -9x + x2 + -60 + 9x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-132 + 19x + 1x2 = 60 + -9x + x2 + -60 + 9x + -1x2

Reorder the terms:
-132 + 19x + 1x2 = 60 + -60 + -9x + 9x + x2 + -1x2

Combine like terms: 60 + -60 = 0
-132 + 19x + 1x2 = 0 + -9x + 9x + x2 + -1x2
-132 + 19x + 1x2 = -9x + 9x + x2 + -1x2

Combine like terms: -9x + 9x = 0
-132 + 19x + 1x2 = 0 + x2 + -1x2
-132 + 19x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-132 + 19x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '132' to each side of the equation.
-132 + 19x + 132 + x2 = 0 + 132

Reorder the terms:
-132 + 132 + 19x + x2 = 0 + 132

Combine like terms: -132 + 132 = 0
0 + 19x + x2 = 0 + 132
19x + x2 = 0 + 132

Combine like terms: 0 + 132 = 132
19x + x2 = 132

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = 132 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 132 + 90.25

Combine like terms: 132 + 90.25 = 222.25
90.25 + 19x + x2 = 222.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 222.25

Calculate the square root of the right side: 14.908051516

Break this problem into two subproblems by setting 
(x + 9.5) equal to 14.908051516 and -14.908051516.

Subproblem 1
x + 9.5 = 14.908051516

Simplifying
x + 9.5 = 14.908051516

Reorder the terms:
9.5 + x = 14.908051516

Solving
9.5 + x = 14.908051516

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 14.908051516 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 14.908051516 + -9.5
x = 14.908051516 + -9.5

Combine like terms: 14.908051516 + -9.5 = 5.408051516
x = 5.408051516

Simplifying
x = 5.408051516

Subproblem 2
x + 9.5 = -14.908051516

Simplifying
x + 9.5 = -14.908051516

Reorder the terms:
9.5 + x = -14.908051516

Solving
9.5 + x = -14.908051516

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -14.908051516 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -14.908051516 + -9.5
x = -14.908051516 + -9.5

Combine like terms: -14.908051516 + -9.5 = -24.408051516
x = -24.408051516

Simplifying
x = -24.408051516

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.408051516, -24.408051516}