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

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


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

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 + -1p + p2) = 0

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

Ignore the factor 4.

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 '(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
Solution
p = {-2, 3}

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