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

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Solution for (x-3)*(x-3)+(x-3)(1-2x)=0 equation: 


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

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

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

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

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) + (x + -3)(1 + -2x) = 0

Reorder the terms:
9 + -6x + x2 + (-3 + x)(1 + -2x) = 0

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

Combine like terms: 6x + 1x = 7x
9 + -6x + x2 + (-3 + 7x + -2x2) = 0

Reorder the terms:
9 + -3 + -6x + 7x + x2 + -2x2 = 0

Combine like terms: 9 + -3 = 6
6 + -6x + 7x + x2 + -2x2 = 0

Combine like terms: -6x + 7x = 1x
6 + 1x + x2 + -2x2 = 0

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

Solving
6 + 1x + -1x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {3, -2}

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