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

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


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

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

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

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

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

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

Remove parenthesis around (2x)
-3 + -2x + x2 = 2x(x + 1)

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 4x + x2) = 0

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

Ignore the factor -1.

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 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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