(3x-2)(x-3)=20

Solution for (3x-2)(x-3)=20 equation:

Simplifying
(3x + -2)(x + -3) = 20

Reorder the terms:
(-2 + 3x)(x + -3) = 20

Reorder the terms:
(-2 + 3x)(-3 + x) = 20

Multiply (-2 + 3x) * (-3 + x)
(-2(-3 + x) + 3x * (-3 + x)) = 20
((-3 * -2 + x * -2) + 3x * (-3 + x)) = 20
((6 + -2x) + 3x * (-3 + x)) = 20
(6 + -2x + (-3 * 3x + x * 3x)) = 20
(6 + -2x + (-9x + 3x2)) = 20

Combine like terms: -2x + -9x = -11x
(6 + -11x + 3x2) = 20

Solving
6 + -11x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
6 + -20 + -11x + 3x2 = 20 + -20

Combine like terms: 6 + -20 = -14
-14 + -11x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-14 + -11x + 3x2 = 0

Factor a trinomial.
(-1 + -1x)(14 + -3x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(14 + -3x)' equal to zero and attempt to solve:

Simplifying
14 + -3x = 0

Solving
14 + -3x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3x = 0 + -14
-3x = 0 + -14

Combine like terms: 0 + -14 = -14
-3x = -14

Divide each side by '-3'.
x = 4.666666667

Simplifying
x = 4.666666667
Solution
x = {-1, 4.666666667}