36=24x-4x^2

Solution for 36=24x-4x^2 equation:

Simplifying
36 = 24x + -4x2

Solving
36 = 24x + -4x2

Solving for variable 'x'.

Reorder the terms:
36 + -24x + 4x2 = 24x + -24x + -4x2 + 4x2

Combine like terms: 24x + -24x = 0
36 + -24x + 4x2 = 0 + -4x2 + 4x2
36 + -24x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
36 + -24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -6x + x2) = 0

Factor a trinomial.
4((3 + -1x)(3 + -1x)) = 0

Ignore the factor 4.
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 '(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
Solution
x = {3, 3}