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

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

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

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

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

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

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

Reorder the terms:
-3 + -1x + 2x2 + x(1 + x) = 0
-3 + -1x + 2x2 + (1 * x + x * x) = 0
-3 + -1x + 2x2 + (1x + x2) = 0

Reorder the terms:
-3 + -1x + 1x + 2x2 + x2 = 0

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

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

Solving
-3 + 3x2 = 0

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + 3x2 = 0 + 3

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

Combine like terms: 0 + 3 = 3
3x2 = 3

Divide each side by '3'.
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}