(7+u)(5u-1)=0

Solution for (7+u)(5u-1)=0 equation:

Simplifying
(7 + u)(5u + -1) = 0

Reorder the terms:
(7 + u)(-1 + 5u) = 0

Multiply (7 + u) * (-1 + 5u)
(7(-1 + 5u) + u(-1 + 5u)) = 0
((-1 * 7 + 5u * 7) + u(-1 + 5u)) = 0
((-7 + 35u) + u(-1 + 5u)) = 0
(-7 + 35u + (-1 * u + 5u * u)) = 0
(-7 + 35u + (-1u + 5u2)) = 0

Combine like terms: 35u + -1u = 34u
(-7 + 34u + 5u2) = 0

Solving
-7 + 34u + 5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + -1u)(1 + -5u) = 0

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

Simplifying
-7 + -1u = 0

Solving
-7 + -1u = 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 + -1u = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1u = 0 + 7
-1u = 0 + 7

Combine like terms: 0 + 7 = 7
-1u = 7

Divide each side by '-1'.
u = -7

Simplifying
u = -7
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 = {-7, 0.2}