3x(x-2)-(x-3)(x-2)=

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


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

Reorder the terms:
3x(-2 + x) + -1(x + -3)(x + -2) = 0
(-2 * 3x + x * 3x) + -1(x + -3)(x + -2) = 0
(-6x + 3x2) + -1(x + -3)(x + -2) = 0

Reorder the terms:
-6x + 3x2 + -1(-3 + x)(x + -2) = 0

Reorder the terms:
-6x + 3x2 + -1(-3 + x)(-2 + x) = 0

Multiply (-3 + x) * (-2 + x)
-6x + 3x2 + -1(-3(-2 + x) + x(-2 + x)) = 0
-6x + 3x2 + -1((-2 * -3 + x * -3) + x(-2 + x)) = 0
-6x + 3x2 + -1((6 + -3x) + x(-2 + x)) = 0
-6x + 3x2 + -1(6 + -3x + (-2 * x + x * x)) = 0
-6x + 3x2 + -1(6 + -3x + (-2x + x2)) = 0

Combine like terms: -3x + -2x = -5x
-6x + 3x2 + -1(6 + -5x + x2) = 0
-6x + 3x2 + (6 * -1 + -5x * -1 + x2 * -1) = 0
-6x + 3x2 + (-6 + 5x + -1x2) = 0

Reorder the terms:
-6 + -6x + 5x + 3x2 + -1x2 = 0

Combine like terms: -6x + 5x = -1x
-6 + -1x + 3x2 + -1x2 = 0

Combine like terms: 3x2 + -1x2 = 2x2
-6 + -1x + 2x2 = 0

Solving
-6 + -1x + 2x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-3 + -2x = 0

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

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.5, 2}

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