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

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


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

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

Multiply (4 + u) * (-7 + 4u)
(4(-7 + 4u) + u(-7 + 4u)) = 0
((-7 * 4 + 4u * 4) + u(-7 + 4u)) = 0
((-28 + 16u) + u(-7 + 4u)) = 0
(-28 + 16u + (-7 * u + 4u * u)) = 0
(-28 + 16u + (-7u + 4u2)) = 0

Combine like terms: 16u + -7u = 9u
(-28 + 9u + 4u2) = 0

Solving
-28 + 9u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4 + -1u)(7 + -4u) = 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 + -4u)' equal to zero and attempt to solve:

Simplifying
7 + -4u = 0

Solving
7 + -4u = 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 + -4u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4u = 0 + -7
-4u = 0 + -7

Combine like terms: 0 + -7 = -7
-4u = -7

Divide each side by '-4'.
u = 1.75

Simplifying
u = 1.75
Solution
u = {-4, 1.75}

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