u^2+21=10x^2+30

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Solution for u^2+21=10x^2+30 equation: 


Simplifying
u2 + 21 = 10x2 + 30

Reorder the terms:
21 + u2 = 10x2 + 30

Reorder the terms:
21 + u2 = 30 + 10x2

Solving
21 + u2 = 30 + 10x2

Solving for variable 'u'.

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

Add '-21' to each side of the equation.
21 + -21 + u2 = 30 + -21 + 10x2

Combine like terms: 21 + -21 = 0
0 + u2 = 30 + -21 + 10x2
u2 = 30 + -21 + 10x2

Combine like terms: 30 + -21 = 9
u2 = 9 + 10x2

Simplifying
u2 = 9 + 10x2

Reorder the terms:
-9 + u2 + -10x2 = 9 + 10x2 + -9 + -10x2

Reorder the terms:
-9 + u2 + -10x2 = 9 + -9 + 10x2 + -10x2

Combine like terms: 9 + -9 = 0
-9 + u2 + -10x2 = 0 + 10x2 + -10x2
-9 + u2 + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-9 + u2 + -10x2 = 0

Factor a trinomial.
(u + -10x)(u + x) = 0


Subproblem 1
Set the factor '(u + -10x)' equal to zero and attempt to solve:

Simplifying
u + -10x = 0

Solving
u + -10x = 0

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

Add '10x' to each side of the equation.
u + -10x + 10x = 0 + 10x

Combine like terms: -10x + 10x = 0
u + 0 = 0 + 10x
u = 0 + 10x
Remove the zero:
u = 10x

Simplifying
u = 10x

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

Simplifying
u + x = 0

Solving
u + x = 0

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

Add '-1x' to each side of the equation.
u + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
u + 0 = 0 + -1x
u = 0 + -1x
Remove the zero:
u = -1x

Simplifying
u = -1x
Solution
u = {10x, -1x}

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