x^2-3x=180-(x+4)(x-5)

Solution for x^2-3x=180-(x+4)(x-5) equation:

Simplifying
x2 + -3x = 180 + -1(x + 4)(x + -5)

Reorder the terms:
-3x + x2 = 180 + -1(x + 4)(x + -5)

Reorder the terms:
-3x + x2 = 180 + -1(4 + x)(x + -5)

Reorder the terms:
-3x + x2 = 180 + -1(4 + x)(-5 + x)

Multiply (4 + x) * (-5 + x)
-3x + x2 = 180 + -1(4(-5 + x) + x(-5 + x))
-3x + x2 = 180 + -1((-5 * 4 + x * 4) + x(-5 + x))
-3x + x2 = 180 + -1((-20 + 4x) + x(-5 + x))
-3x + x2 = 180 + -1(-20 + 4x + (-5 * x + x * x))
-3x + x2 = 180 + -1(-20 + 4x + (-5x + x2))

Combine like terms: 4x + -5x = -1x
-3x + x2 = 180 + -1(-20 + -1x + x2)
-3x + x2 = 180 + (-20 * -1 + -1x * -1 + x2 * -1)
-3x + x2 = 180 + (20 + 1x + -1x2)

Combine like terms: 180 + 20 = 200
-3x + x2 = 200 + 1x + -1x2

Solving
-3x + x2 = 200 + 1x + -1x2

Solving for variable 'x'.

Reorder the terms:
-200 + -3x + -1x + x2 + x2 = 200 + 1x + -1x2 + -200 + -1x + x2

Combine like terms: -3x + -1x = -4x
-200 + -4x + x2 + x2 = 200 + 1x + -1x2 + -200 + -1x + x2

Combine like terms: x2 + x2 = 2x2
-200 + -4x + 2x2 = 200 + 1x + -1x2 + -200 + -1x + x2

Reorder the terms:
-200 + -4x + 2x2 = 200 + -200 + 1x + -1x + -1x2 + x2

Combine like terms: 200 + -200 = 0
-200 + -4x + 2x2 = 0 + 1x + -1x + -1x2 + x2
-200 + -4x + 2x2 = 1x + -1x + -1x2 + x2

Combine like terms: 1x + -1x = 0
-200 + -4x + 2x2 = 0 + -1x2 + x2
-200 + -4x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-200 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-100 + -2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-100 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-100 + -2x + x2 = 0

Solving
-100 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -2x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + -2x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -2x + x2 = 0 + 100
-2x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
-2x + x2 = 100

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 = 100 + 1

Reorder the terms:
1 + -2x + x2 = 100 + 1

Combine like terms: 100 + 1 = 101
1 + -2x + x2 = 101

Factor a perfect square on the left side:
(x + -1)(x + -1) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(x + -1) equal to 10.049875621 and -10.049875621.

Subproblem 1
x + -1 = 10.049875621

Simplifying
x + -1 = 10.049875621

Reorder the terms:
-1 + x = 10.049875621

Solving
-1 + x = 10.049875621

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 = 10.049875621 + 1

Combine like terms: -1 + 1 = 0
0 + x = 10.049875621 + 1
x = 10.049875621 + 1

Combine like terms: 10.049875621 + 1 = 11.049875621
x = 11.049875621

Simplifying
x = 11.049875621

Subproblem 2
x + -1 = -10.049875621

Simplifying
x + -1 = -10.049875621

Reorder the terms:
-1 + x = -10.049875621

Solving
-1 + x = -10.049875621

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 = -10.049875621 + 1

Combine like terms: -1 + 1 = 0
0 + x = -10.049875621 + 1
x = -10.049875621 + 1

Combine like terms: -10.049875621 + 1 = -9.049875621
x = -9.049875621

Simplifying
x = -9.049875621

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.049875621, -9.049875621}
Solution
x = {11.049875621, -9.049875621}