3p^2+40=9p+70

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Solution for 3p^2+40=9p+70 equation: 


Simplifying
3p2 + 40 = 9p + 70

Reorder the terms:
40 + 3p2 = 9p + 70

Reorder the terms:
40 + 3p2 = 70 + 9p

Solving
40 + 3p2 = 70 + 9p

Solving for variable 'p'.

Reorder the terms:
40 + -70 + -9p + 3p2 = 70 + 9p + -70 + -9p

Combine like terms: 40 + -70 = -30
-30 + -9p + 3p2 = 70 + 9p + -70 + -9p

Reorder the terms:
-30 + -9p + 3p2 = 70 + -70 + 9p + -9p

Combine like terms: 70 + -70 = 0
-30 + -9p + 3p2 = 0 + 9p + -9p
-30 + -9p + 3p2 = 9p + -9p

Combine like terms: 9p + -9p = 0
-30 + -9p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -3p + p2) = 0

Factor a trinomial.
3((-2 + -1p)(5 + -1p)) = 0

Ignore the factor 3.

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 '(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 = {-2, 5}

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