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

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


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

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

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

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

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

Reorder the terms:
-3 + 2x + x2 = (2 + x)(x + -3) * 1

Reorder the terms:
-3 + 2x + x2 = (2 + x)(-3 + x) * 1

Reorder the terms for easier multiplication:
-3 + 2x + x2 = 1(2 + x)(-3 + x)

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

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

Solving
-3 + 2x + x2 = -6 + -1x + 1x2

Solving for variable 'x'.

Reorder the terms:
-3 + 6 + 2x + x + x2 + -1x2 = -6 + -1x + 1x2 + 6 + x + -1x2

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

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

Combine like terms: x2 + -1x2 = 0
3 + 3x + 0 = -6 + -1x + 1x2 + 6 + x + -1x2
3 + 3x = -6 + -1x + 1x2 + 6 + x + -1x2

Reorder the terms:
3 + 3x = -6 + 6 + -1x + x + 1x2 + -1x2

Combine like terms: -6 + 6 = 0
3 + 3x = 0 + -1x + x + 1x2 + -1x2
3 + 3x = -1x + x + 1x2 + -1x2

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + x) = 0

Ignore the factor 3.

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-1}

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