(u-6)(u+4)=-21

Solution for (u-6)(u+4)=-21 equation:

Simplifying
(u + -6)(u + 4) = -21

Reorder the terms:
(-6 + u)(u + 4) = -21

Reorder the terms:
(-6 + u)(4 + u) = -21

Multiply (-6 + u) * (4 + u)
(-6(4 + u) + u(4 + u)) = -21
((4 * -6 + u * -6) + u(4 + u)) = -21
((-24 + -6u) + u(4 + u)) = -21
(-24 + -6u + (4 * u + u * u)) = -21
(-24 + -6u + (4u + u2)) = -21

Combine like terms: -6u + 4u = -2u
(-24 + -2u + u2) = -21

Solving
-24 + -2u + u2 = -21

Solving for variable 'u'.

Reorder the terms:
-24 + 21 + -2u + u2 = -21 + 21

Combine like terms: -24 + 21 = -3
-3 + -2u + u2 = -21 + 21

Combine like terms: -21 + 21 = 0
-3 + -2u + u2 = 0

Factor a trinomial.
(-1 + -1u)(3 + -1u) = 0

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

Simplifying
-1 + -1u = 0

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

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

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

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

Simplifying
u = -1
Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 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 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {-1, 3}