(3u-7)(2+u)=0

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Solution for (3u-7)(2+u)=0 equation: 


Simplifying
(3u + -7)(2 + u) = 0

Reorder the terms:
(-7 + 3u)(2 + u) = 0

Multiply (-7 + 3u) * (2 + u)
(-7(2 + u) + 3u * (2 + u)) = 0
((2 * -7 + u * -7) + 3u * (2 + u)) = 0
((-14 + -7u) + 3u * (2 + u)) = 0
(-14 + -7u + (2 * 3u + u * 3u)) = 0
(-14 + -7u + (6u + 3u2)) = 0

Combine like terms: -7u + 6u = -1u
(-14 + -1u + 3u2) = 0

Solving
-14 + -1u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-2 + -1u)(7 + -3u) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -3u)' equal to zero and attempt to solve:

Simplifying
7 + -3u = 0

Solving
7 + -3u = 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 + -3u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3u = 0 + -7
-3u = 0 + -7

Combine like terms: 0 + -7 = -7
-3u = -7

Divide each side by '-3'.
u = 2.333333333

Simplifying
u = 2.333333333
Solution
u = {-2, 2.333333333}

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