(2u-7)(4+u)=0

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Solution for (2u-7)(4+u)=0 equation: 


Simplifying
(2u + -7)(4 + u) = 0

Reorder the terms:
(-7 + 2u)(4 + u) = 0

Multiply (-7 + 2u) * (4 + u)
(-7(4 + u) + 2u * (4 + u)) = 0
((4 * -7 + u * -7) + 2u * (4 + u)) = 0
((-28 + -7u) + 2u * (4 + u)) = 0
(-28 + -7u + (4 * 2u + u * 2u)) = 0
(-28 + -7u + (8u + 2u2)) = 0

Combine like terms: -7u + 8u = 1u
(-28 + 1u + 2u2) = 0

Solving
-28 + 1u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4 + -1u)(7 + -2u) = 0


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

Simplifying
-4 + -1u = 0

Solving
-4 + -1u = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1u = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1u = 0 + 4
-1u = 0 + 4

Combine like terms: 0 + 4 = 4
-1u = 4

Divide each side by '-1'.
u = -4

Simplifying
u = -4

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

Simplifying
7 + -2u = 0

Solving
7 + -2u = 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 + -2u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2u = 0 + -7
-2u = 0 + -7

Combine like terms: 0 + -7 = -7
-2u = -7

Divide each side by '-2'.
u = 3.5

Simplifying
u = 3.5
Solution
u = {-4, 3.5}

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