0=4u^2+5u-21

Solution for 0=4u^2+5u-21 equation:

Simplifying
0 = 4u2 + 5u + -21

Reorder the terms:
0 = -21 + 5u + 4u2

Solving
0 = -21 + 5u + 4u2

Solving for variable 'u'.

Combine like terms: 0 + 21 = 21
21 + -5u + -4u2 = -21 + 5u + 4u2 + 21 + -5u + -4u2

Reorder the terms:
21 + -5u + -4u2 = -21 + 21 + 5u + -5u + 4u2 + -4u2

Combine like terms: -21 + 21 = 0
21 + -5u + -4u2 = 0 + 5u + -5u + 4u2 + -4u2
21 + -5u + -4u2 = 5u + -5u + 4u2 + -4u2

Combine like terms: 5u + -5u = 0
21 + -5u + -4u2 = 0 + 4u2 + -4u2
21 + -5u + -4u2 = 4u2 + -4u2

Combine like terms: 4u2 + -4u2 = 0
21 + -5u + -4u2 = 0

Factor a trinomial.
(7 + -4u)(3 + u) = 0

Subproblem 1
Set the factor '(7 + -4u)' equal to zero and attempt to solve:

Simplifying
7 + -4u = 0

Solving
7 + -4u = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4u = 0 + -7
-4u = 0 + -7

Combine like terms: 0 + -7 = -7
-4u = -7

Divide each side by '-4'.
u = 1.75

Simplifying
u = 1.75
Subproblem 2
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 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 + u = 0 + -3

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

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

Simplifying
u = -3
Solution
u = {1.75, -3}