24u+6=30u^2

Solution for 24u+6=30u^2 equation:

Simplifying
24u + 6 = 30u2

Reorder the terms:
6 + 24u = 30u2

Solving
6 + 24u = 30u2

Solving for variable 'u'.

Combine like terms: 30u2 + -30u2 = 0
6 + 24u + -30u2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 4u + -5u2) = 0

Factor a trinomial.
6((1 + -1u)(1 + 5u)) = 0

Ignore the factor 6.
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 '(1 + 5u)' equal to zero and attempt to solve:

Simplifying
1 + 5u = 0

Solving
1 + 5u = 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 + 5u = 0 + -1

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

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

Divide each side by '5'.
u = -0.2

Simplifying
u = -0.2
Solution
u = {1, -0.2}