3p^2+4p=-p^2+24

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Solution for 3p^2+4p=-p^2+24 equation: 


Simplifying
3p2 + 4p = -1p2 + 24

Reorder the terms:
4p + 3p2 = -1p2 + 24

Reorder the terms:
4p + 3p2 = 24 + -1p2

Solving
4p + 3p2 = 24 + -1p2

Solving for variable 'p'.

Reorder the terms:
-24 + 4p + 3p2 + p2 = 24 + -1p2 + -24 + p2

Combine like terms: 3p2 + p2 = 4p2
-24 + 4p + 4p2 = 24 + -1p2 + -24 + p2

Reorder the terms:
-24 + 4p + 4p2 = 24 + -24 + -1p2 + p2

Combine like terms: 24 + -24 = 0
-24 + 4p + 4p2 = 0 + -1p2 + p2
-24 + 4p + 4p2 = -1p2 + p2

Combine like terms: -1p2 + p2 = 0
-24 + 4p + 4p2 = 0

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

Factor a trinomial.
4((-3 + -1p)(2 + -1p)) = 0

Ignore the factor 4.

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

Simplifying
-3 + -1p = 0

Solving
-3 + -1p = 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 + -1p = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1p = 0 + 3
-1p = 0 + 3

Combine like terms: 0 + 3 = 3
-1p = 3

Divide each side by '-1'.
p = -3

Simplifying
p = -3

Subproblem 2
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
Solution
p = {-3, 2}

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