(x-3)(2-x)=-5x(2-x)

Solution for (x-3)(2-x)=-5x(2-x) equation:

Simplifying
(x + -3)(2 + -1x) = -5x(2 + -1x)

Reorder the terms:
(-3 + x)(2 + -1x) = -5x(2 + -1x)

Multiply (-3 + x) * (2 + -1x)
(-3(2 + -1x) + x(2 + -1x)) = -5x(2 + -1x)
((2 * -3 + -1x * -3) + x(2 + -1x)) = -5x(2 + -1x)
((-6 + 3x) + x(2 + -1x)) = -5x(2 + -1x)
(-6 + 3x + (2 * x + -1x * x)) = -5x(2 + -1x)
(-6 + 3x + (2x + -1x2)) = -5x(2 + -1x)

Combine like terms: 3x + 2x = 5x
(-6 + 5x + -1x2) = -5x(2 + -1x)
-6 + 5x + -1x2 = (2 * -5x + -1x * -5x)
-6 + 5x + -1x2 = (-10x + 5x2)

Solving
-6 + 5x + -1x2 = -10x + 5x2

Solving for variable 'x'.

Reorder the terms:
-6 + 5x + 10x + -1x2 + -5x2 = -10x + 5x2 + 10x + -5x2

Combine like terms: 5x + 10x = 15x
-6 + 15x + -1x2 + -5x2 = -10x + 5x2 + 10x + -5x2

Combine like terms: -1x2 + -5x2 = -6x2
-6 + 15x + -6x2 = -10x + 5x2 + 10x + -5x2

Reorder the terms:
-6 + 15x + -6x2 = -10x + 10x + 5x2 + -5x2

Combine like terms: -10x + 10x = 0
-6 + 15x + -6x2 = 0 + 5x2 + -5x2
-6 + 15x + -6x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-6 + 15x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 5x + -2x2) = 0

Factor a trinomial.
3((-2 + x)(1 + -2x)) = 0

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {2, 0.5}