30-6p^2=2p^2+4p+6

Solution for 30-6p^2=2p^2+4p+6 equation:

Simplifying
30 + -6p2 = 2p2 + 4p + 6

Reorder the terms:
30 + -6p2 = 6 + 4p + 2p2

Solving
30 + -6p2 = 6 + 4p + 2p2

Solving for variable 'p'.

Reorder the terms:
30 + -6 + -4p + -6p2 + -2p2 = 6 + 4p + 2p2 + -6 + -4p + -2p2

Combine like terms: 30 + -6 = 24
24 + -4p + -6p2 + -2p2 = 6 + 4p + 2p2 + -6 + -4p + -2p2

Combine like terms: -6p2 + -2p2 = -8p2
24 + -4p + -8p2 = 6 + 4p + 2p2 + -6 + -4p + -2p2

Reorder the terms:
24 + -4p + -8p2 = 6 + -6 + 4p + -4p + 2p2 + -2p2

Combine like terms: 6 + -6 = 0
24 + -4p + -8p2 = 0 + 4p + -4p + 2p2 + -2p2
24 + -4p + -8p2 = 4p + -4p + 2p2 + -2p2

Combine like terms: 4p + -4p = 0
24 + -4p + -8p2 = 0 + 2p2 + -2p2
24 + -4p + -8p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
24 + -4p + -8p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -1p + -2p2) = 0

Factor a trinomial.
4((3 + -2p)(2 + p)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -2p)' equal to zero and attempt to solve:

Simplifying
3 + -2p = 0

Solving
3 + -2p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2p = 0 + -3

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

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

Divide each side by '-2'.
p = 1.5

Simplifying
p = 1.5
Subproblem 2
Set the factor '(2 + p)' equal to zero and attempt to solve:

Simplifying
2 + p = 0

Solving
2 + p = 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 + p = 0 + -2

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

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

Simplifying
p = -2
Solution
p = {1.5, -2}