(x-2)*(x-3)=56

Solution for (x-2)*(x-3)=56 equation:

Simplifying
(x + -2)(x + -3) = 56

Reorder the terms:
(-2 + x)(x + -3) = 56

Reorder the terms:
(-2 + x)(-3 + x) = 56

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) = 56
((-3 * -2 + x * -2) + x(-3 + x)) = 56
((6 + -2x) + x(-3 + x)) = 56
(6 + -2x + (-3 * x + x * x)) = 56
(6 + -2x + (-3x + x2)) = 56

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) = 56

Solving
6 + -5x + x2 = 56

Solving for variable 'x'.

Reorder the terms:
6 + -56 + -5x + x2 = 56 + -56

Combine like terms: 6 + -56 = -50
-50 + -5x + x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-50 + -5x + x2 = 0

Factor a trinomial.
(-5 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-5, 10}