u(4u-3)=5u(u+2)

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Solution for u(4u-3)=5u(u+2) equation: 


Simplifying
u(4u + -3) = 5u(u + 2)

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

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

Solving
-3u + 4u2 = 10u + 5u2

Solving for variable 'u'.

Reorder the terms:
-3u + -10u + 4u2 + -5u2 = 10u + 5u2 + -10u + -5u2

Combine like terms: -3u + -10u = -13u
-13u + 4u2 + -5u2 = 10u + 5u2 + -10u + -5u2

Combine like terms: 4u2 + -5u2 = -1u2
-13u + -1u2 = 10u + 5u2 + -10u + -5u2

Reorder the terms:
-13u + -1u2 = 10u + -10u + 5u2 + -5u2

Combine like terms: 10u + -10u = 0
-13u + -1u2 = 0 + 5u2 + -5u2
-13u + -1u2 = 5u2 + -5u2

Combine like terms: 5u2 + -5u2 = 0
-13u + -1u2 = 0

Factor out the Greatest Common Factor (GCF), '-1u'.
-1u(13 + u) = 0

Ignore the factor -1.

Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0

Subproblem 2
Set the factor '(13 + u)' equal to zero and attempt to solve:

Simplifying
13 + u = 0

Solving
13 + u = 0

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

Add '-13' to each side of the equation.
13 + -13 + u = 0 + -13

Combine like terms: 13 + -13 = 0
0 + u = 0 + -13
u = 0 + -13

Combine like terms: 0 + -13 = -13
u = -13

Simplifying
u = -13
Solution
u = {0, -13}

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