x-4+4+(x-2)(x+1)=0

Solution for x-4+4+(x-2)(x+1)=0 equation:

Simplifying
x + -4 + 4 + (x + -2)(x + 1) = 0

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

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

Multiply (-2 + x) * (1 + x)
x + -4 + 4 + (-2(1 + x) + x(1 + x)) = 0
x + -4 + 4 + ((1 * -2 + x * -2) + x(1 + x)) = 0
x + -4 + 4 + ((-2 + -2x) + x(1 + x)) = 0
x + -4 + 4 + (-2 + -2x + (1 * x + x * x)) = 0
x + -4 + 4 + (-2 + -2x + (1x + x2)) = 0

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

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

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

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

Solving
-2 + x2 = 0

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x2 = 0 + 2

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

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

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}