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

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

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

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

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

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

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

Reorder the terms:
-6 + -4x + 2x2 + -1(1 + x) = 0
-6 + -4x + 2x2 + (1 * -1 + x * -1) = 0
-6 + -4x + 2x2 + (-1 + -1x) = 0

Reorder the terms:
-6 + -1 + -4x + -1x + 2x2 = 0

Combine like terms: -6 + -1 = -7
-7 + -4x + -1x + 2x2 = 0

Combine like terms: -4x + -1x = -5x
-7 + -5x + 2x2 = 0

Solving
-7 + -5x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(7 + -2x) = 0

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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-1, 3.5}