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

Solution for 3(x-5)2(2x-1)= equation:

Simplifying
3(x + -5) * 2(2x + -1) = 0

Reorder the terms:
3(-5 + x) * 2(2x + -1) = 0

Reorder the terms:
3(-5 + x) * 2(-1 + 2x) = 0

Reorder the terms for easier multiplication:
3 * 2(-5 + x)(-1 + 2x) = 0

Multiply 3 * 2
6(-5 + x)(-1 + 2x) = 0

Multiply (-5 + x) * (-1 + 2x)
6(-5(-1 + 2x) + x(-1 + 2x)) = 0
6((-1 * -5 + 2x * -5) + x(-1 + 2x)) = 0
6((5 + -10x) + x(-1 + 2x)) = 0
6(5 + -10x + (-1 * x + 2x * x)) = 0
6(5 + -10x + (-1x + 2x2)) = 0

Combine like terms: -10x + -1x = -11x
6(5 + -11x + 2x2) = 0
(5 * 6 + -11x * 6 + 2x2 * 6) = 0
(30 + -66x + 12x2) = 0

Solving
30 + -66x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(5 + -11x + 2x2) = 0

Factor a trinomial.
6((1 + -2x)(5 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0.5, 5}