(2u+7)(3u-1)=0

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Solution for (2u+7)(3u-1)=0 equation: 


Simplifying
(2u + 7)(3u + -1) = 0

Reorder the terms:
(7 + 2u)(3u + -1) = 0

Reorder the terms:
(7 + 2u)(-1 + 3u) = 0

Multiply (7 + 2u) * (-1 + 3u)
(7(-1 + 3u) + 2u * (-1 + 3u)) = 0
((-1 * 7 + 3u * 7) + 2u * (-1 + 3u)) = 0
((-7 + 21u) + 2u * (-1 + 3u)) = 0
(-7 + 21u + (-1 * 2u + 3u * 2u)) = 0
(-7 + 21u + (-2u + 6u2)) = 0

Combine like terms: 21u + -2u = 19u
(-7 + 19u + 6u2) = 0

Solving
-7 + 19u + 6u2 = 0

Solving for variable 'u'.

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


Subproblem 1
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

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

Simplifying
1 + -3u = 0

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

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

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

Divide each side by '-3'.
u = 0.3333333333

Simplifying
u = 0.3333333333
Solution
u = {-3.5, 0.3333333333}

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