x(7-x)=12

Solution for x(7-x)=12 equation:

Simplifying
x(7 + -1x) = 12
(7 * x + -1x * x) = 12
(7x + -1x2) = 12

Solving
7x + -1x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 7x + -1x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 7x + -1x2 = 0

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

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
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 = {4, 3}