3x(x+8)=60

Solution for 3x(x+8)=60 equation:

Simplifying
3x(x + 8) = 60

Reorder the terms:
3x(8 + x) = 60
(8 * 3x + x * 3x) = 60
(24x + 3x2) = 60

Solving
24x + 3x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + 24x + 3x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + 8x + x2) = 0

Factor a trinomial.
3((-10 + -1x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-10, 2}