-4p^2=8p-12

Solution for -4p^2=8p-12 equation:

Simplifying
-4p2 = 8p + -12

Reorder the terms:
-4p2 = -12 + 8p

Solving
-4p2 = -12 + 8p

Solving for variable 'p'.

Reorder the terms:
12 + -8p + -4p2 = -12 + 8p + 12 + -8p

Reorder the terms:
12 + -8p + -4p2 = -12 + 12 + 8p + -8p

Combine like terms: -12 + 12 = 0
12 + -8p + -4p2 = 0 + 8p + -8p
12 + -8p + -4p2 = 8p + -8p

Combine like terms: 8p + -8p = 0
12 + -8p + -4p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -2p + -1p2) = 0

Factor a trinomial.
4((1 + -1p)(3 + p)) = 0

Ignore the factor 4.
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 '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 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 + p = 0 + -3

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

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

Simplifying
p = -3
Solution
p = {1, -3}