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

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

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

Reorder the terms:
5(-3 + x) = 2x(3 + -1x)
(-3 * 5 + x * 5) = 2x(3 + -1x)
(-15 + 5x) = 2x(3 + -1x)
-15 + 5x = (3 * 2x + -1x * 2x)
-15 + 5x = (6x + -2x2)

Solving
-15 + 5x = 6x + -2x2

Solving for variable 'x'.

Combine like terms: 5x + -6x = -1x
-15 + -1x + 2x2 = 6x + -2x2 + -6x + 2x2

Reorder the terms:
-15 + -1x + 2x2 = 6x + -6x + -2x2 + 2x2

Combine like terms: 6x + -6x = 0
-15 + -1x + 2x2 = 0 + -2x2 + 2x2
-15 + -1x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-15 + -1x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(3 + -1x) = 0

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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2.5, 3}