F(x)=x*(x+1)

Solution for F(x)=x*(x+1) equation:

Simplifying
F(x) = x(x + 1)

Multiply F * x
xF = x(x + 1)

Reorder the terms:
xF = x(1 + x)
xF = (1 * x + x * x)
xF = (1x + x2)

Solving
xF = 1x + x2

Solving for variable 'x'.

Reorder the terms:
-1x + xF + -1x2 = 1x + x2 + -1x + -1x2

Reorder the terms:
-1x + xF + -1x2 = 1x + -1x + x2 + -1x2

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + F + -1x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + F + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + F + -1x = 0

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

Reorder the terms:
-1 + 1 + F + -1x = 0 + 1

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

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

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

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

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

Simplifying
x = -1 + F
Solution
x = {0, -1 + F}