3(2-3x)=4x(x-1)

Solution for 3(2-3x)=4x(x-1) equation:

Simplifying
3(2 + -3x) = 4x(x + -1)
(2 * 3 + -3x * 3) = 4x(x + -1)
(6 + -9x) = 4x(x + -1)

Reorder the terms:
6 + -9x = 4x(-1 + x)
6 + -9x = (-1 * 4x + x * 4x)
6 + -9x = (-4x + 4x2)

Solving
6 + -9x = -4x + 4x2

Solving for variable 'x'.

Combine like terms: -9x + 4x = -5x
6 + -5x + -4x2 = -4x + 4x2 + 4x + -4x2

Reorder the terms:
6 + -5x + -4x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
6 + -5x + -4x2 = 0 + 4x2 + -4x2
6 + -5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + -5x + -4x2 = 0

Factor a trinomial.
(3 + -4x)(2 + x) = 0

Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Subproblem 2
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
Solution
x = {0.75, -2}