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

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


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

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

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

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

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

Solving
-6 + 1x + x2 = 2x

Solving for variable 'x'.

Reorder the terms:
-6 + 1x + -2x + x2 = 2x + -2x

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

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

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-2, 3}

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