3a^2+a=a^2+10a+11

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Solution for 3a^2+a=a^2+10a+11 equation: 


Simplifying
3a2 + a = a2 + 10a + 11

Reorder the terms:
a + 3a2 = a2 + 10a + 11

Reorder the terms:
a + 3a2 = 11 + 10a + a2

Solving
a + 3a2 = 11 + 10a + a2

Solving for variable 'a'.

Reorder the terms:
-11 + a + -10a + 3a2 + -1a2 = 11 + 10a + a2 + -11 + -10a + -1a2

Combine like terms: a + -10a = -9a
-11 + -9a + 3a2 + -1a2 = 11 + 10a + a2 + -11 + -10a + -1a2

Combine like terms: 3a2 + -1a2 = 2a2
-11 + -9a + 2a2 = 11 + 10a + a2 + -11 + -10a + -1a2

Reorder the terms:
-11 + -9a + 2a2 = 11 + -11 + 10a + -10a + a2 + -1a2

Combine like terms: 11 + -11 = 0
-11 + -9a + 2a2 = 0 + 10a + -10a + a2 + -1a2
-11 + -9a + 2a2 = 10a + -10a + a2 + -1a2

Combine like terms: 10a + -10a = 0
-11 + -9a + 2a2 = 0 + a2 + -1a2
-11 + -9a + 2a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-11 + -9a + 2a2 = 0

Factor a trinomial.
(-1 + -1a)(11 + -2a) = 0


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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1a = 0 + 1
-1a = 0 + 1

Combine like terms: 0 + 1 = 1
-1a = 1

Divide each side by '-1'.
a = -1

Simplifying
a = -1

Subproblem 2
Set the factor '(11 + -2a)' equal to zero and attempt to solve:

Simplifying
11 + -2a = 0

Solving
11 + -2a = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2a = 0 + -11
-2a = 0 + -11

Combine like terms: 0 + -11 = -11
-2a = -11

Divide each side by '-2'.
a = 5.5

Simplifying
a = 5.5
Solution
a = {-1, 5.5}

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