3p^2-13=7+21p-2p^2

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Solution for 3p^2-13=7+21p-2p^2 equation: 


Simplifying
3p2 + -13 = 7 + 21p + -2p2

Reorder the terms:
-13 + 3p2 = 7 + 21p + -2p2

Solving
-13 + 3p2 = 7 + 21p + -2p2

Solving for variable 'p'.

Reorder the terms:
-13 + -7 + -21p + 3p2 + 2p2 = 7 + 21p + -2p2 + -7 + -21p + 2p2

Combine like terms: -13 + -7 = -20
-20 + -21p + 3p2 + 2p2 = 7 + 21p + -2p2 + -7 + -21p + 2p2

Combine like terms: 3p2 + 2p2 = 5p2
-20 + -21p + 5p2 = 7 + 21p + -2p2 + -7 + -21p + 2p2

Reorder the terms:
-20 + -21p + 5p2 = 7 + -7 + 21p + -21p + -2p2 + 2p2

Combine like terms: 7 + -7 = 0
-20 + -21p + 5p2 = 0 + 21p + -21p + -2p2 + 2p2
-20 + -21p + 5p2 = 21p + -21p + -2p2 + 2p2

Combine like terms: 21p + -21p = 0
-20 + -21p + 5p2 = 0 + -2p2 + 2p2
-20 + -21p + 5p2 = -2p2 + 2p2

Combine like terms: -2p2 + 2p2 = 0
-20 + -21p + 5p2 = 0

Factor a trinomial.
(-4 + -5p)(5 + -1p) = 0


Subproblem 1
Set the factor '(-4 + -5p)' equal to zero and attempt to solve:

Simplifying
-4 + -5p = 0

Solving
-4 + -5p = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5p = 0 + 4
-5p = 0 + 4

Combine like terms: 0 + 4 = 4
-5p = 4

Divide each side by '-5'.
p = -0.8

Simplifying
p = -0.8

Subproblem 2
Set the factor '(5 + -1p)' equal to zero and attempt to solve:

Simplifying
5 + -1p = 0

Solving
5 + -1p = 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 + -1p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1p = 0 + -5
-1p = 0 + -5

Combine like terms: 0 + -5 = -5
-1p = -5

Divide each side by '-1'.
p = 5

Simplifying
p = 5
Solution
p = {-0.8, 5}

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