(x-3)(x-3)+(x-2)(x+4)=1

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Solution for (x-3)(x-3)+(x-2)(x+4)=1 equation: 


Simplifying
(x + -3)(x + -3) + (x + -2)(x + 4) = 1

Reorder the terms:
(-3 + x)(x + -3) + (x + -2)(x + 4) = 1

Reorder the terms:
(-3 + x)(-3 + x) + (x + -2)(x + 4) = 1

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) + (x + -2)(x + 4) = 1
((-3 * -3 + x * -3) + x(-3 + x)) + (x + -2)(x + 4) = 1
((9 + -3x) + x(-3 + x)) + (x + -2)(x + 4) = 1
(9 + -3x + (-3 * x + x * x)) + (x + -2)(x + 4) = 1
(9 + -3x + (-3x + x2)) + (x + -2)(x + 4) = 1

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) + (x + -2)(x + 4) = 1

Reorder the terms:
9 + -6x + x2 + (-2 + x)(x + 4) = 1

Reorder the terms:
9 + -6x + x2 + (-2 + x)(4 + x) = 1

Multiply (-2 + x) * (4 + x)
9 + -6x + x2 + (-2(4 + x) + x(4 + x)) = 1
9 + -6x + x2 + ((4 * -2 + x * -2) + x(4 + x)) = 1
9 + -6x + x2 + ((-8 + -2x) + x(4 + x)) = 1
9 + -6x + x2 + (-8 + -2x + (4 * x + x * x)) = 1
9 + -6x + x2 + (-8 + -2x + (4x + x2)) = 1

Combine like terms: -2x + 4x = 2x
9 + -6x + x2 + (-8 + 2x + x2) = 1

Reorder the terms:
9 + -8 + -6x + 2x + x2 + x2 = 1

Combine like terms: 9 + -8 = 1
1 + -6x + 2x + x2 + x2 = 1

Combine like terms: -6x + 2x = -4x
1 + -4x + x2 + x2 = 1

Combine like terms: x2 + x2 = 2x2
1 + -4x + 2x2 = 1

Add '-1' to each side of the equation.
1 + -4x + -1 + 2x2 = 1 + -1

Reorder the terms:
1 + -1 + -4x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + -4x + 2x2 = 1 + -1
-4x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-4x + 2x2 = 0

Solving
-4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-2 + x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, 2}

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