4u^2=-7u-3

Solution for 4u^2=-7u-3 equation:

Simplifying
4u2 = -7u + -3

Reorder the terms:
4u2 = -3 + -7u

Solving
4u2 = -3 + -7u

Solving for variable 'u'.

Reorder the terms:
3 + 7u + 4u2 = -3 + -7u + 3 + 7u

Reorder the terms:
3 + 7u + 4u2 = -3 + 3 + -7u + 7u

Combine like terms: -3 + 3 = 0
3 + 7u + 4u2 = 0 + -7u + 7u
3 + 7u + 4u2 = -7u + 7u

Combine like terms: -7u + 7u = 0
3 + 7u + 4u2 = 0

Factor a trinomial.
(1 + u)(3 + 4u) = 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 '(3 + 4u)' equal to zero and attempt to solve:

Simplifying
3 + 4u = 0

Solving
3 + 4u = 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 + 4u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4u = 0 + -3
4u = 0 + -3

Combine like terms: 0 + -3 = -3
4u = -3

Divide each side by '4'.
u = -0.75

Simplifying
u = -0.75
Solution
u = {-1, -0.75}