9p^2=7+6p+8p^2

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Solution for 9p^2=7+6p+8p^2 equation: 


Simplifying
9p2 = 7 + 6p + 8p2

Solving
9p2 = 7 + 6p + 8p2

Solving for variable 'p'.

Reorder the terms:
-7 + -6p + 9p2 + -8p2 = 7 + 6p + 8p2 + -7 + -6p + -8p2

Combine like terms: 9p2 + -8p2 = 1p2
-7 + -6p + 1p2 = 7 + 6p + 8p2 + -7 + -6p + -8p2

Reorder the terms:
-7 + -6p + 1p2 = 7 + -7 + 6p + -6p + 8p2 + -8p2

Combine like terms: 7 + -7 = 0
-7 + -6p + 1p2 = 0 + 6p + -6p + 8p2 + -8p2
-7 + -6p + 1p2 = 6p + -6p + 8p2 + -8p2

Combine like terms: 6p + -6p = 0
-7 + -6p + 1p2 = 0 + 8p2 + -8p2
-7 + -6p + 1p2 = 8p2 + -8p2

Combine like terms: 8p2 + -8p2 = 0
-7 + -6p + 1p2 = 0

Factor a trinomial.
(-1 + -1p)(7 + -1p) = 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 '(7 + -1p)' equal to zero and attempt to solve:

Simplifying
7 + -1p = 0

Solving
7 + -1p = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1p = 0 + -7
-1p = 0 + -7

Combine like terms: 0 + -7 = -7
-1p = -7

Divide each side by '-1'.
p = 7

Simplifying
p = 7
Solution
p = {-1, 7}

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