2x(5x+20)=120

Solution for 2x(5x+20)=120 equation:

Simplifying
2x(5x + 20) = 120

Reorder the terms:
2x(20 + 5x) = 120
(20 * 2x + 5x * 2x) = 120
(40x + 10x2) = 120

Solving
40x + 10x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 40x + 10x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 40x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-12 + 4x + x2) = 0

Factor a trinomial.
10((-6 + -1x)(2 + -1x)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 2}