(x-3)*(3x-2)=(x+3)*(2-3x)

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Solution for (x-3)*(3x-2)=(x+3)*(2-3x) equation:


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

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

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

Multiply (-3 + x) * (-2 + 3x)
(-3(-2 + 3x) + x(-2 + 3x)) = (x + 3)(2 + -3x)
((-2 * -3 + 3x * -3) + x(-2 + 3x)) = (x + 3)(2 + -3x)
((6 + -9x) + x(-2 + 3x)) = (x + 3)(2 + -3x)
(6 + -9x + (-2 * x + 3x * x)) = (x + 3)(2 + -3x)
(6 + -9x + (-2x + 3x2)) = (x + 3)(2 + -3x)

Combine like terms: -9x + -2x = -11x
(6 + -11x + 3x2) = (x + 3)(2 + -3x)

Reorder the terms:
6 + -11x + 3x2 = (3 + x)(2 + -3x)

Multiply (3 + x) * (2 + -3x)
6 + -11x + 3x2 = (3(2 + -3x) + x(2 + -3x))
6 + -11x + 3x2 = ((2 * 3 + -3x * 3) + x(2 + -3x))
6 + -11x + 3x2 = ((6 + -9x) + x(2 + -3x))
6 + -11x + 3x2 = (6 + -9x + (2 * x + -3x * x))
6 + -11x + 3x2 = (6 + -9x + (2x + -3x2))

Combine like terms: -9x + 2x = -7x
6 + -11x + 3x2 = (6 + -7x + -3x2)

Add '-6' to each side of the equation.
6 + -11x + -6 + 3x2 = 6 + -7x + -6 + -3x2

Reorder the terms:
6 + -6 + -11x + 3x2 = 6 + -7x + -6 + -3x2

Combine like terms: 6 + -6 = 0
0 + -11x + 3x2 = 6 + -7x + -6 + -3x2
-11x + 3x2 = 6 + -7x + -6 + -3x2

Reorder the terms:
-11x + 3x2 = 6 + -6 + -7x + -3x2

Combine like terms: 6 + -6 = 0
-11x + 3x2 = 0 + -7x + -3x2
-11x + 3x2 = -7x + -3x2

Solving
-11x + 3x2 = -7x + -3x2

Solving for variable 'x'.

Reorder the terms:
-11x + 7x + 3x2 + 3x2 = -7x + -3x2 + 7x + 3x2

Combine like terms: -11x + 7x = -4x
-4x + 3x2 + 3x2 = -7x + -3x2 + 7x + 3x2

Combine like terms: 3x2 + 3x2 = 6x2
-4x + 6x2 = -7x + -3x2 + 7x + 3x2

Reorder the terms:
-4x + 6x2 = -7x + 7x + -3x2 + 3x2

Combine like terms: -7x + 7x = 0
-4x + 6x2 = 0 + -3x2 + 3x2
-4x + 6x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-4x + 6x2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 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 + 3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

Divide each side by '3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0, 0.6666666667}

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