(3x-9)(x-2)-(x-3)=

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Solution for (3x-9)(x-2)-(x-3)= equation: 


Simplifying
(3x + -9)(x + -2) + -1(x + -3) = 0

Reorder the terms:
(-9 + 3x)(x + -2) + -1(x + -3) = 0

Reorder the terms:
(-9 + 3x)(-2 + x) + -1(x + -3) = 0

Multiply (-9 + 3x) * (-2 + x)
(-9(-2 + x) + 3x * (-2 + x)) + -1(x + -3) = 0
((-2 * -9 + x * -9) + 3x * (-2 + x)) + -1(x + -3) = 0
((18 + -9x) + 3x * (-2 + x)) + -1(x + -3) = 0
(18 + -9x + (-2 * 3x + x * 3x)) + -1(x + -3) = 0
(18 + -9x + (-6x + 3x2)) + -1(x + -3) = 0

Combine like terms: -9x + -6x = -15x
(18 + -15x + 3x2) + -1(x + -3) = 0

Reorder the terms:
18 + -15x + 3x2 + -1(-3 + x) = 0
18 + -15x + 3x2 + (-3 * -1 + x * -1) = 0
18 + -15x + 3x2 + (3 + -1x) = 0

Reorder the terms:
18 + 3 + -15x + -1x + 3x2 = 0

Combine like terms: 18 + 3 = 21
21 + -15x + -1x + 3x2 = 0

Combine like terms: -15x + -1x = -16x
21 + -16x + 3x2 = 0

Solving
21 + -16x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -3x)(3 + -1x) = 0


Subproblem 1
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333

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 = {2.333333333, 3}

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