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

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


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

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

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

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

Combine like terms: -5u + 7u = 2u
(-35 + 2u + u2) = 0

Solving
-35 + 2u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-7 + -1u)(5 + -1u) = 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 '(5 + -1u)' equal to zero and attempt to solve:

Simplifying
5 + -1u = 0

Solving
5 + -1u = 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 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

Simplifying
u = 5
Solution
u = {-7, 5}

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