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

Solution for 4-(x+3)(x+2)=x(1-x) equation:

Simplifying
4 + -1(x + 3)(x + 2) = x(1 + -1x)

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

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

Multiply (3 + x) * (2 + x)
4 + -1(3(2 + x) + x(2 + x)) = x(1 + -1x)
4 + -1((2 * 3 + x * 3) + x(2 + x)) = x(1 + -1x)
4 + -1((6 + 3x) + x(2 + x)) = x(1 + -1x)
4 + -1(6 + 3x + (2 * x + x * x)) = x(1 + -1x)
4 + -1(6 + 3x + (2x + x2)) = x(1 + -1x)

Combine like terms: 3x + 2x = 5x
4 + -1(6 + 5x + x2) = x(1 + -1x)
4 + (6 * -1 + 5x * -1 + x2 * -1) = x(1 + -1x)
4 + (-6 + -5x + -1x2) = x(1 + -1x)

Combine like terms: 4 + -6 = -2
-2 + -5x + -1x2 = x(1 + -1x)
-2 + -5x + -1x2 = (1 * x + -1x * x)
-2 + -5x + -1x2 = (1x + -1x2)

Add 'x2' to each side of the equation.
-2 + -5x + -1x2 + x2 = 1x + -1x2 + x2

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

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

Solving
-2 + -5x = 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
-2 + -5x + -1x = 1x + -1x

Combine like terms: -5x + -1x = -6x
-2 + -6x = 1x + -1x

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

Add '2' to each side of the equation.
-2 + 2 + -6x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -6x = 0 + 2
-6x = 0 + 2

Combine like terms: 0 + 2 = 2
-6x = 2

Divide each side by '-6'.
x = -0.3333333333

Simplifying
x = -0.3333333333