(x-23)(55-x)=87

Solution for (x-23)(55-x)=87 equation:

Simplifying
(x + -23)(55 + -1x) = 87

Reorder the terms:
(-23 + x)(55 + -1x) = 87

Multiply (-23 + x) * (55 + -1x)
(-23(55 + -1x) + x(55 + -1x)) = 87
((55 * -23 + -1x * -23) + x(55 + -1x)) = 87
((-1265 + 23x) + x(55 + -1x)) = 87
(-1265 + 23x + (55 * x + -1x * x)) = 87
(-1265 + 23x + (55x + -1x2)) = 87

Combine like terms: 23x + 55x = 78x
(-1265 + 78x + -1x2) = 87

Solving
-1265 + 78x + -1x2 = 87

Solving for variable 'x'.

Reorder the terms:
-1265 + -87 + 78x + -1x2 = 87 + -87

Combine like terms: -1265 + -87 = -1352
-1352 + 78x + -1x2 = 87 + -87

Combine like terms: 87 + -87 = 0
-1352 + 78x + -1x2 = 0

Factor a trinomial.
(-52 + x)(26 + -1x) = 0

Subproblem 1
Set the factor '(-52 + x)' equal to zero and attempt to solve:

Simplifying
-52 + x = 0

Solving
-52 + x = 0

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

Add '52' to each side of the equation.
-52 + 52 + x = 0 + 52

Combine like terms: -52 + 52 = 0
0 + x = 0 + 52
x = 0 + 52

Combine like terms: 0 + 52 = 52
x = 52

Simplifying
x = 52
Subproblem 2
Set the factor '(26 + -1x)' equal to zero and attempt to solve:

Simplifying
26 + -1x = 0

Solving
26 + -1x = 0

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

Add '-26' to each side of the equation.
26 + -26 + -1x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -1x = 0 + -26
-1x = 0 + -26

Combine like terms: 0 + -26 = -26
-1x = -26

Divide each side by '-1'.
x = 26

Simplifying
x = 26
Solution
x = {52, 26}