2u(20u-40)=120

Solution for 2u(20u-40)=120 equation:

Simplifying
2u(20u + -40) = 120

Reorder the terms:
2u(-40 + 20u) = 120
(-40 * 2u + 20u * 2u) = 120
(-80u + 40u2) = 120

Solving
-80u + 40u2 = 120

Solving for variable 'u'.

Reorder the terms:
-120 + -80u + 40u2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + -80u + 40u2 = 0

Factor out the Greatest Common Factor (GCF), '40'.
40(-3 + -2u + u2) = 0

Factor a trinomial.
40((-1 + -1u)(3 + -1u)) = 0

Ignore the factor 40.
Subproblem 1
Set the factor '(-1 + -1u)' equal to zero and attempt to solve:

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1u = 0 + 1
-1u = 0 + 1

Combine like terms: 0 + 1 = 1
-1u = 1

Divide each side by '-1'.
u = -1

Simplifying
u = -1
Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {-1, 3}