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

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


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

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

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

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

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

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

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

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

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

Solving
-3 + -2x + x2 = -6 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3 + 6 + -2x + 4x + x2 + -2x2 = -6 + -4x + 2x2 + 6 + 4x + -2x2

Combine like terms: -3 + 6 = 3
3 + -2x + 4x + x2 + -2x2 = -6 + -4x + 2x2 + 6 + 4x + -2x2

Combine like terms: -2x + 4x = 2x
3 + 2x + x2 + -2x2 = -6 + -4x + 2x2 + 6 + 4x + -2x2

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

Reorder the terms:
3 + 2x + -1x2 = -6 + 6 + -4x + 4x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
3 + 2x + -1x2 = 0 + -4x + 4x + 2x2 + -2x2
3 + 2x + -1x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
3 + 2x + -1x2 = 0 + 2x2 + -2x2
3 + 2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 2x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(1 + 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 '(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 = {3, -1}

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