3(x-2)(2x-1)=105

Solution for 3(x-2)(2x-1)=105 equation:

Simplifying
3(x + -2)(2x + -1) = 105

Reorder the terms:
3(-2 + x)(2x + -1) = 105

Reorder the terms:
3(-2 + x)(-1 + 2x) = 105

Multiply (-2 + x) * (-1 + 2x)
3(-2(-1 + 2x) + x(-1 + 2x)) = 105
3((-1 * -2 + 2x * -2) + x(-1 + 2x)) = 105
3((2 + -4x) + x(-1 + 2x)) = 105
3(2 + -4x + (-1 * x + 2x * x)) = 105
3(2 + -4x + (-1x + 2x2)) = 105

Combine like terms: -4x + -1x = -5x
3(2 + -5x + 2x2) = 105
(2 * 3 + -5x * 3 + 2x2 * 3) = 105
(6 + -15x + 6x2) = 105

Solving
6 + -15x + 6x2 = 105

Solving for variable 'x'.

Reorder the terms:
6 + -105 + -15x + 6x2 = 105 + -105

Combine like terms: 6 + -105 = -99
-99 + -15x + 6x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-99 + -15x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-33 + -5x + 2x2) = 0

Factor a trinomial.
3((-3 + -1x)(11 + -2x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {-3, 5.5}