3(5-2x)x=6

Solution for 3(5-2x)x=6 equation:

Simplifying
3(5 + -2x) * x = 6

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

Solving
15x + -6x2 = 6

Solving for variable 'x'.

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

Combine like terms: 6 + -6 = 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}