P+10=11P^2-P+1

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Solution for P+10=11P^2-P+1 equation: 


Simplifying
P + 10 = 11P2 + -1P + 1

Reorder the terms:
10 + P = 11P2 + -1P + 1

Reorder the terms:
10 + P = 1 + -1P + 11P2

Solving
10 + P = 1 + -1P + 11P2

Solving for variable 'P'.

Reorder the terms:
10 + -1 + P + P + -11P2 = 1 + -1P + 11P2 + -1 + P + -11P2

Combine like terms: 10 + -1 = 9
9 + P + P + -11P2 = 1 + -1P + 11P2 + -1 + P + -11P2

Combine like terms: P + P = 2P
9 + 2P + -11P2 = 1 + -1P + 11P2 + -1 + P + -11P2

Reorder the terms:
9 + 2P + -11P2 = 1 + -1 + -1P + P + 11P2 + -11P2

Combine like terms: 1 + -1 = 0
9 + 2P + -11P2 = 0 + -1P + P + 11P2 + -11P2
9 + 2P + -11P2 = -1P + P + 11P2 + -11P2

Combine like terms: -1P + P = 0
9 + 2P + -11P2 = 0 + 11P2 + -11P2
9 + 2P + -11P2 = 11P2 + -11P2

Combine like terms: 11P2 + -11P2 = 0
9 + 2P + -11P2 = 0

Factor a trinomial.
(1 + -1P)(9 + 11P) = 0


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

Simplifying
1 + -1P = 0

Solving
1 + -1P = 0

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

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

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

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

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

Simplifying
P = 1

Subproblem 2
Set the factor '(9 + 11P)' equal to zero and attempt to solve:

Simplifying
9 + 11P = 0

Solving
9 + 11P = 0

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

Add '-9' to each side of the equation.
9 + -9 + 11P = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 11P = 0 + -9
11P = 0 + -9

Combine like terms: 0 + -9 = -9
11P = -9

Divide each side by '11'.
P = -0.8181818182

Simplifying
P = -0.8181818182
Solution
P = {1, -0.8181818182}

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