4*9=x*(9+x)

Solution for 4*9=x*(9+x) equation:

Simplifying
4 * 9 = x(9 + x)

Multiply 4 * 9
36 = x(9 + x)
36 = (9 * x + x * x)
36 = (9x + x2)

Solving
36 = 9x + x2

Solving for variable 'x'.

Reorder the terms:
36 + -9x + -1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
36 + -9x + -1x2 = 0 + x2 + -1x2
36 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
36 + -9x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(12 + x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {3, -12}