(4u-6)(7-u)=0

Solution for (4u-6)(7-u)=0 equation:

Simplifying
(4u + -6)(7 + -1u) = 0

Reorder the terms:
(-6 + 4u)(7 + -1u) = 0

Multiply (-6 + 4u) * (7 + -1u)
(-6(7 + -1u) + 4u * (7 + -1u)) = 0
((7 * -6 + -1u * -6) + 4u * (7 + -1u)) = 0
((-42 + 6u) + 4u * (7 + -1u)) = 0
(-42 + 6u + (7 * 4u + -1u * 4u)) = 0
(-42 + 6u + (28u + -4u2)) = 0

Combine like terms: 6u + 28u = 34u
(-42 + 34u + -4u2) = 0

Solving
-42 + 34u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 17u + -2u2) = 0

Factor a trinomial.
2((-7 + u)(3 + -2u)) = 0

Ignore the factor 2.
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 '(3 + -2u)' equal to zero and attempt to solve:

Simplifying
3 + -2u = 0

Solving
3 + -2u = 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 + -2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2u = 0 + -3
-2u = 0 + -3

Combine like terms: 0 + -3 = -3
-2u = -3

Divide each side by '-2'.
u = 1.5

Simplifying
u = 1.5
Solution
u = {7, 1.5}