p^2+p-6=-2p^2+4

Solution for p^2+p-6=-2p^2+4 equation:

Simplifying
p2 + p + -6 = -2p2 + 4

Reorder the terms:
-6 + p + p2 = -2p2 + 4

Reorder the terms:
-6 + p + p2 = 4 + -2p2

Solving
-6 + p + p2 = 4 + -2p2

Solving for variable 'p'.

Reorder the terms:
-6 + -4 + p + p2 + 2p2 = 4 + -2p2 + -4 + 2p2

Combine like terms: -6 + -4 = -10
-10 + p + p2 + 2p2 = 4 + -2p2 + -4 + 2p2

Combine like terms: p2 + 2p2 = 3p2
-10 + p + 3p2 = 4 + -2p2 + -4 + 2p2

Reorder the terms:
-10 + p + 3p2 = 4 + -4 + -2p2 + 2p2

Combine like terms: 4 + -4 = 0
-10 + p + 3p2 = 0 + -2p2 + 2p2
-10 + p + 3p2 = -2p2 + 2p2

Combine like terms: -2p2 + 2p2 = 0
-10 + p + 3p2 = 0

Factor a trinomial.
(-2 + -1p)(5 + -3p) = 0

Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve:

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

Simplifying
p = -2
Subproblem 2
Set the factor '(5 + -3p)' equal to zero and attempt to solve:

Simplifying
5 + -3p = 0

Solving
5 + -3p = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3p = 0 + -5
-3p = 0 + -5

Combine like terms: 0 + -5 = -5
-3p = -5

Divide each side by '-3'.
p = 1.666666667

Simplifying
p = 1.666666667
Solution
p = {-2, 1.666666667}