(5u^2)+2=-7u

Solution for (5u^2)+2=-7u equation:

Simplifying
(5u2) + 2 = -7u

Reorder the terms:
2 + (5u2) = -7u

Solving
2 + (5u2) = -7u

Solving for variable 'u'.

Reorder the terms:
2 + 7u + (5u2) = -7u + 7u

Combine like terms: -7u + 7u = 0
2 + 7u + (5u2) = 0

Factor a trinomial.
(1 + u)(2 + 5u) = 0

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

Simplifying
1 + u = 0

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

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

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

Simplifying
u = -1
Subproblem 2
Set the factor '(2 + 5u)' equal to zero and attempt to solve:

Simplifying
2 + 5u = 0

Solving
2 + 5u = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5u = 0 + -2
5u = 0 + -2

Combine like terms: 0 + -2 = -2
5u = -2

Divide each side by '5'.
u = -0.4

Simplifying
u = -0.4
Solution
u = {-1, -0.4}