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

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


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

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

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

Multiply (-2 + 3x) * (-3 + x)
(-2(-3 + x) + 3x * (-3 + x)) + 2 = 0
((-3 * -2 + x * -2) + 3x * (-3 + x)) + 2 = 0
((6 + -2x) + 3x * (-3 + x)) + 2 = 0
(6 + -2x + (-3 * 3x + x * 3x)) + 2 = 0
(6 + -2x + (-9x + 3x2)) + 2 = 0

Combine like terms: -2x + -9x = -11x
(6 + -11x + 3x2) + 2 = 0

Reorder the terms:
6 + 2 + -11x + 3x2 = 0

Combine like terms: 6 + 2 = 8
8 + -11x + 3x2 = 0

Solving
8 + -11x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(8 + -3x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {1, 2.666666667}

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