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

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

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

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

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

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

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

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

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

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

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

Add 'x' to each side of the equation.
-6 + -1x + x + 2x2 = 3 + -1x + x + x2

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

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

Solving
-6 + 2x2 = 3 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
-6 + 2x2 + -1x2 = 3 + x2 + -1x2

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

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

Add '6' to each side of the equation.
-6 + 6 + 1x2 = 3 + 6

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

Combine like terms: 3 + 6 = 9
1x2 = 9

Divide each side by '1'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}