3p^2+16=-3p^2+8+19p

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Solution for 3p^2+16=-3p^2+8+19p equation: 


Simplifying
3p2 + 16 = -3p2 + 8 + 19p

Reorder the terms:
16 + 3p2 = -3p2 + 8 + 19p

Reorder the terms:
16 + 3p2 = 8 + 19p + -3p2

Solving
16 + 3p2 = 8 + 19p + -3p2

Solving for variable 'p'.

Reorder the terms:
16 + -8 + -19p + 3p2 + 3p2 = 8 + 19p + -3p2 + -8 + -19p + 3p2

Combine like terms: 16 + -8 = 8
8 + -19p + 3p2 + 3p2 = 8 + 19p + -3p2 + -8 + -19p + 3p2

Combine like terms: 3p2 + 3p2 = 6p2
8 + -19p + 6p2 = 8 + 19p + -3p2 + -8 + -19p + 3p2

Reorder the terms:
8 + -19p + 6p2 = 8 + -8 + 19p + -19p + -3p2 + 3p2

Combine like terms: 8 + -8 = 0
8 + -19p + 6p2 = 0 + 19p + -19p + -3p2 + 3p2
8 + -19p + 6p2 = 19p + -19p + -3p2 + 3p2

Combine like terms: 19p + -19p = 0
8 + -19p + 6p2 = 0 + -3p2 + 3p2
8 + -19p + 6p2 = -3p2 + 3p2

Combine like terms: -3p2 + 3p2 = 0
8 + -19p + 6p2 = 0

Factor a trinomial.
(1 + -2p)(8 + -3p) = 0


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

Simplifying
1 + -2p = 0

Solving
1 + -2p = 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 + -2p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2p = 0 + -1
-2p = 0 + -1

Combine like terms: 0 + -1 = -1
-2p = -1

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5

Subproblem 2
Set the factor '(8 + -3p)' equal to zero and attempt to solve:

Simplifying
8 + -3p = 0

Solving
8 + -3p = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3p = 0 + -8
-3p = 0 + -8

Combine like terms: 0 + -8 = -8
-3p = -8

Divide each side by '-3'.
p = 2.666666667

Simplifying
p = 2.666666667
Solution
p = {0.5, 2.666666667}

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