60(x+12)=10x(x)

Solution for 60(x+12)=10x(x) equation:

Simplifying
60(x + 12) = 10x(x)

Reorder the terms:
60(12 + x) = 10x(x)
(12 * 60 + x * 60) = 10x(x)
(720 + 60x) = 10x(x)

Multiply x * x
720 + 60x = 10x2

Solving
720 + 60x = 10x2

Solving for variable 'x'.

Combine like terms: 10x2 + -10x2 = 0
720 + 60x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(72 + 6x + -1x2) = 0

Factor a trinomial.
10((12 + -1x)(6 + x)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 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 + -1x = 0 + -12

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

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

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {12, -6}