(5u-6)(7-u)=0

Solution for (5u-6)(7-u)=0 equation:

Simplifying
(5u + -6)(7 + -1u) = 0

Reorder the terms:
(-6 + 5u)(7 + -1u) = 0

Multiply (-6 + 5u) * (7 + -1u)
(-6(7 + -1u) + 5u * (7 + -1u)) = 0
((7 * -6 + -1u * -6) + 5u * (7 + -1u)) = 0
((-42 + 6u) + 5u * (7 + -1u)) = 0
(-42 + 6u + (7 * 5u + -1u * 5u)) = 0
(-42 + 6u + (35u + -5u2)) = 0

Combine like terms: 6u + 35u = 41u
(-42 + 41u + -5u2) = 0

Solving
-42 + 41u + -5u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + u)(6 + -5u) = 0

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

Simplifying
-7 + u = 0

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

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

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

Simplifying
u = 7
Subproblem 2
Set the factor '(6 + -5u)' equal to zero and attempt to solve:

Simplifying
6 + -5u = 0

Solving
6 + -5u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5u = 0 + -6
-5u = 0 + -6

Combine like terms: 0 + -6 = -6
-5u = -6

Divide each side by '-5'.
u = 1.2

Simplifying
u = 1.2
Solution
u = {7, 1.2}