(x-2)(x-3)=306

Solution for (x-2)(x-3)=306 equation:

Simplifying
(x + -2)(x + -3) = 306

Reorder the terms:
(-2 + x)(x + -3) = 306

Reorder the terms:
(-2 + x)(-3 + x) = 306

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) = 306
((-3 * -2 + x * -2) + x(-3 + x)) = 306
((6 + -2x) + x(-3 + x)) = 306
(6 + -2x + (-3 * x + x * x)) = 306
(6 + -2x + (-3x + x2)) = 306

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) = 306

Solving
6 + -5x + x2 = 306

Solving for variable 'x'.

Reorder the terms:
6 + -306 + -5x + x2 = 306 + -306

Combine like terms: 6 + -306 = -300
-300 + -5x + x2 = 306 + -306

Combine like terms: 306 + -306 = 0
-300 + -5x + x2 = 0

Factor a trinomial.
(-15 + -1x)(20 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {-15, 20}