3p+q^2+5q-102=p-2q^2+3q+71

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Solution for 3p+q^2+5q-102=p-2q^2+3q+71 equation:


Simplifying
3p + q2 + 5q + -102 = p + -2q2 + 3q + 71

Reorder the terms:
-102 + 3p + 5q + q2 = p + -2q2 + 3q + 71

Reorder the terms:
-102 + 3p + 5q + q2 = 71 + p + 3q + -2q2

Solving
-102 + 3p + 5q + q2 = 71 + p + 3q + -2q2

Solving for variable 'p'.

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

Add '-1p' to each side of the equation.
-102 + 3p + 5q + -1p + q2 = 71 + p + 3q + -1p + -2q2

Reorder the terms:
-102 + 3p + -1p + 5q + q2 = 71 + p + 3q + -1p + -2q2

Combine like terms: 3p + -1p = 2p
-102 + 2p + 5q + q2 = 71 + p + 3q + -1p + -2q2

Reorder the terms:
-102 + 2p + 5q + q2 = 71 + p + -1p + 3q + -2q2

Combine like terms: p + -1p = 0
-102 + 2p + 5q + q2 = 71 + 0 + 3q + -2q2
-102 + 2p + 5q + q2 = 71 + 3q + -2q2

Add '102' to each side of the equation.
-102 + 2p + 5q + 102 + q2 = 71 + 3q + 102 + -2q2

Reorder the terms:
-102 + 102 + 2p + 5q + q2 = 71 + 3q + 102 + -2q2

Combine like terms: -102 + 102 = 0
0 + 2p + 5q + q2 = 71 + 3q + 102 + -2q2
2p + 5q + q2 = 71 + 3q + 102 + -2q2

Reorder the terms:
2p + 5q + q2 = 71 + 102 + 3q + -2q2

Combine like terms: 71 + 102 = 173
2p + 5q + q2 = 173 + 3q + -2q2

Add '-5q' to each side of the equation.
2p + 5q + -5q + q2 = 173 + 3q + -5q + -2q2

Combine like terms: 5q + -5q = 0
2p + 0 + q2 = 173 + 3q + -5q + -2q2
2p + q2 = 173 + 3q + -5q + -2q2

Combine like terms: 3q + -5q = -2q
2p + q2 = 173 + -2q + -2q2

Add '-1q2' to each side of the equation.
2p + q2 + -1q2 = 173 + -2q + -2q2 + -1q2

Combine like terms: q2 + -1q2 = 0
2p + 0 = 173 + -2q + -2q2 + -1q2
2p = 173 + -2q + -2q2 + -1q2

Combine like terms: -2q2 + -1q2 = -3q2
2p = 173 + -2q + -3q2

Divide each side by '2'.
p = 86.5 + -1q + -1.5q2

Simplifying
p = 86.5 + -1q + -1.5q2

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