(x+3)*(x-23)=360

Solution for (x+3)*(x-23)=360 equation:

Simplifying
(x + 3)(x + -23) = 360

Reorder the terms:
(3 + x)(x + -23) = 360

Reorder the terms:
(3 + x)(-23 + x) = 360

Multiply (3 + x) * (-23 + x)
(3(-23 + x) + x(-23 + x)) = 360
((-23 * 3 + x * 3) + x(-23 + x)) = 360
((-69 + 3x) + x(-23 + x)) = 360
(-69 + 3x + (-23 * x + x * x)) = 360
(-69 + 3x + (-23x + x2)) = 360

Combine like terms: 3x + -23x = -20x
(-69 + -20x + x2) = 360

Solving
-69 + -20x + x2 = 360

Solving for variable 'x'.

Reorder the terms:
-69 + -360 + -20x + x2 = 360 + -360

Combine like terms: -69 + -360 = -429
-429 + -20x + x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-429 + -20x + x2 = 0

Factor a trinomial.
(-13 + -1x)(33 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
Subproblem 2
Set the factor '(33 + -1x)' equal to zero and attempt to solve:

Simplifying
33 + -1x = 0

Solving
33 + -1x = 0

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

Add '-33' to each side of the equation.
33 + -33 + -1x = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -1x = 0 + -33
-1x = 0 + -33

Combine like terms: 0 + -33 = -33
-1x = -33

Divide each side by '-1'.
x = 33

Simplifying
x = 33
Solution
x = {-13, 33}