6P-4=3-P^2

Solution for 6P-4=3-P^2 equation:

Simplifying
6P + -4 = 3 + -1P2

Reorder the terms:
-4 + 6P = 3 + -1P2

Solving
-4 + 6P = 3 + -1P2

Solving for variable 'P'.

Reorder the terms:
-4 + -3 + 6P + P2 = 3 + -1P2 + -3 + P2

Combine like terms: -4 + -3 = -7
-7 + 6P + P2 = 3 + -1P2 + -3 + P2

Reorder the terms:
-7 + 6P + P2 = 3 + -3 + -1P2 + P2

Combine like terms: 3 + -3 = 0
-7 + 6P + P2 = 0 + -1P2 + P2
-7 + 6P + P2 = -1P2 + P2

Combine like terms: -1P2 + P2 = 0
-7 + 6P + P2 = 0

Factor a trinomial.
(-7 + -1P)(1 + -1P) = 0

Subproblem 1
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
Subproblem 2
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
Solution
P = {-7, 1}