2u(3u+2)=5(3u+2)

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Solution for 2u(3u+2)=5(3u+2) equation: 


Simplifying
2u(3u + 2) = 5(3u + 2)

Reorder the terms:
2u(2 + 3u) = 5(3u + 2)
(2 * 2u + 3u * 2u) = 5(3u + 2)
(4u + 6u2) = 5(3u + 2)

Reorder the terms:
4u + 6u2 = 5(2 + 3u)
4u + 6u2 = (2 * 5 + 3u * 5)
4u + 6u2 = (10 + 15u)

Solving
4u + 6u2 = 10 + 15u

Solving for variable 'u'.

Reorder the terms:
-10 + 4u + -15u + 6u2 = 10 + 15u + -10 + -15u

Combine like terms: 4u + -15u = -11u
-10 + -11u + 6u2 = 10 + 15u + -10 + -15u

Reorder the terms:
-10 + -11u + 6u2 = 10 + -10 + 15u + -15u

Combine like terms: 10 + -10 = 0
-10 + -11u + 6u2 = 0 + 15u + -15u
-10 + -11u + 6u2 = 15u + -15u

Combine like terms: 15u + -15u = 0
-10 + -11u + 6u2 = 0

Factor a trinomial.
(-2 + -3u)(5 + -2u) = 0


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

Simplifying
-2 + -3u = 0

Solving
-2 + -3u = 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 + -3u = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3u = 0 + 2
-3u = 0 + 2

Combine like terms: 0 + 2 = 2
-3u = 2

Divide each side by '-3'.
u = -0.6666666667

Simplifying
u = -0.6666666667

Subproblem 2
Set the factor '(5 + -2u)' equal to zero and attempt to solve:

Simplifying
5 + -2u = 0

Solving
5 + -2u = 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 + -2u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2u = 0 + -5
-2u = 0 + -5

Combine like terms: 0 + -5 = -5
-2u = -5

Divide each side by '-2'.
u = 2.5

Simplifying
u = 2.5
Solution
u = {-0.6666666667, 2.5}

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