5u^2+14u-3=20u^2+31u-7

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Solution for 5u^2+14u-3=20u^2+31u-7 equation: 


Simplifying
5u2 + 14u + -3 = 20u2 + 31u + -7

Reorder the terms:
-3 + 14u + 5u2 = 20u2 + 31u + -7

Reorder the terms:
-3 + 14u + 5u2 = -7 + 31u + 20u2

Solving
-3 + 14u + 5u2 = -7 + 31u + 20u2

Solving for variable 'u'.

Reorder the terms:
-3 + 7 + 14u + -31u + 5u2 + -20u2 = -7 + 31u + 20u2 + 7 + -31u + -20u2

Combine like terms: -3 + 7 = 4
4 + 14u + -31u + 5u2 + -20u2 = -7 + 31u + 20u2 + 7 + -31u + -20u2

Combine like terms: 14u + -31u = -17u
4 + -17u + 5u2 + -20u2 = -7 + 31u + 20u2 + 7 + -31u + -20u2

Combine like terms: 5u2 + -20u2 = -15u2
4 + -17u + -15u2 = -7 + 31u + 20u2 + 7 + -31u + -20u2

Reorder the terms:
4 + -17u + -15u2 = -7 + 7 + 31u + -31u + 20u2 + -20u2

Combine like terms: -7 + 7 = 0
4 + -17u + -15u2 = 0 + 31u + -31u + 20u2 + -20u2
4 + -17u + -15u2 = 31u + -31u + 20u2 + -20u2

Combine like terms: 31u + -31u = 0
4 + -17u + -15u2 = 0 + 20u2 + -20u2
4 + -17u + -15u2 = 20u2 + -20u2

Combine like terms: 20u2 + -20u2 = 0
4 + -17u + -15u2 = 0

Factor a trinomial.
(1 + -5u)(4 + 3u) = 0


Subproblem 1
Set the factor '(1 + -5u)' equal to zero and attempt to solve:

Simplifying
1 + -5u = 0

Solving
1 + -5u = 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 + -5u = 0 + -1

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

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

Divide each side by '-5'.
u = 0.2

Simplifying
u = 0.2

Subproblem 2
Set the factor '(4 + 3u)' equal to zero and attempt to solve:

Simplifying
4 + 3u = 0

Solving
4 + 3u = 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 + 3u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3u = 0 + -4
3u = 0 + -4

Combine like terms: 0 + -4 = -4
3u = -4

Divide each side by '3'.
u = -1.333333333

Simplifying
u = -1.333333333
Solution
u = {0.2, -1.333333333}

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