4(u-5)(-u+2)=0

Solution for 4(u-5)(-u+2)=0 equation:

Simplifying
4(u + -5)(-1u + 2) = 0

Reorder the terms:
4(-5 + u)(-1u + 2) = 0

Reorder the terms:
4(-5 + u)(2 + -1u) = 0

Multiply (-5 + u) * (2 + -1u)
4(-5(2 + -1u) + u(2 + -1u)) = 0
4((2 * -5 + -1u * -5) + u(2 + -1u)) = 0
4((-10 + 5u) + u(2 + -1u)) = 0
4(-10 + 5u + (2 * u + -1u * u)) = 0
4(-10 + 5u + (2u + -1u2)) = 0

Combine like terms: 5u + 2u = 7u
4(-10 + 7u + -1u2) = 0
(-10 * 4 + 7u * 4 + -1u2 * 4) = 0
(-40 + 28u + -4u2) = 0

Solving
-40 + 28u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 7u + -1u2) = 0

Factor a trinomial.
4((-5 + u)(2 + -1u)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + u)' equal to zero and attempt to solve:

Simplifying
-5 + u = 0

Solving
-5 + u = 0

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

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

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

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

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

Simplifying
2 + -1u = 0

Solving
2 + -1u = 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 + -1u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1u = 0 + -2
-1u = 0 + -2

Combine like terms: 0 + -2 = -2
-1u = -2

Divide each side by '-1'.
u = 2

Simplifying
u = 2
Solution
u = {5, 2}