60-(x(6-x)+x(10-x))=30

Solution for 60-(x(6-x)+x(10-x))=30 equation:

Simplifying
60 + -1(x(6 + -1x) + x(10 + -1x)) = 30
60 + -1((6 * x + -1x * x) + x(10 + -1x)) = 30
60 + -1((6x + -1x2) + x(10 + -1x)) = 30
60 + -1(6x + -1x2 + (10 * x + -1x * x)) = 30
60 + -1(6x + -1x2 + (10x + -1x2)) = 30

Reorder the terms:
60 + -1(6x + 10x + -1x2 + -1x2) = 30

Combine like terms: 6x + 10x = 16x
60 + -1(16x + -1x2 + -1x2) = 30

Combine like terms: -1x2 + -1x2 = -2x2
60 + -1(16x + -2x2) = 30
60 + (16x * -1 + -2x2 * -1) = 30
60 + (-16x + 2x2) = 30

Solving
60 + -16x + 2x2 = 30

Solving for variable 'x'.

Reorder the terms:
60 + -30 + -16x + 2x2 = 30 + -30

Combine like terms: 60 + -30 = 30
30 + -16x + 2x2 = 30 + -30

Combine like terms: 30 + -30 = 0
30 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -8x + x2) = 0

Factor a trinomial.
2((3 + -1x)(5 + -1x)) = 0

Ignore the factor 2.
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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {3, 5}