(5q-15)(q+4)=(q^2+4q)(q+6)+(2q-27)(q+6)

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Solution for (5q-15)(q+4)=(q^2+4q)(q+6)+(2q-27)(q+6) equation:


Simplifying
(5q + -15)(q + 4) = (q2 + 4q)(q + 6) + (2q + -27)(q + 6)

Reorder the terms:
(-15 + 5q)(q + 4) = (q2 + 4q)(q + 6) + (2q + -27)(q + 6)

Reorder the terms:
(-15 + 5q)(4 + q) = (q2 + 4q)(q + 6) + (2q + -27)(q + 6)

Multiply (-15 + 5q) * (4 + q)
(-15(4 + q) + 5q * (4 + q)) = (q2 + 4q)(q + 6) + (2q + -27)(q + 6)
((4 * -15 + q * -15) + 5q * (4 + q)) = (q2 + 4q)(q + 6) + (2q + -27)(q + 6)
((-60 + -15q) + 5q * (4 + q)) = (q2 + 4q)(q + 6) + (2q + -27)(q + 6)
(-60 + -15q + (4 * 5q + q * 5q)) = (q2 + 4q)(q + 6) + (2q + -27)(q + 6)
(-60 + -15q + (20q + 5q2)) = (q2 + 4q)(q + 6) + (2q + -27)(q + 6)

Combine like terms: -15q + 20q = 5q
(-60 + 5q + 5q2) = (q2 + 4q)(q + 6) + (2q + -27)(q + 6)

Reorder the terms:
-60 + 5q + 5q2 = (4q + q2)(q + 6) + (2q + -27)(q + 6)

Reorder the terms:
-60 + 5q + 5q2 = (4q + q2)(6 + q) + (2q + -27)(q + 6)

Multiply (4q + q2) * (6 + q)
-60 + 5q + 5q2 = (4q * (6 + q) + q2(6 + q)) + (2q + -27)(q + 6)
-60 + 5q + 5q2 = ((6 * 4q + q * 4q) + q2(6 + q)) + (2q + -27)(q + 6)
-60 + 5q + 5q2 = ((24q + 4q2) + q2(6 + q)) + (2q + -27)(q + 6)
-60 + 5q + 5q2 = (24q + 4q2 + (6 * q2 + q * q2)) + (2q + -27)(q + 6)
-60 + 5q + 5q2 = (24q + 4q2 + (6q2 + q3)) + (2q + -27)(q + 6)

Combine like terms: 4q2 + 6q2 = 10q2
-60 + 5q + 5q2 = (24q + 10q2 + q3) + (2q + -27)(q + 6)

Reorder the terms:
-60 + 5q + 5q2 = 24q + 10q2 + q3 + (-27 + 2q)(q + 6)

Reorder the terms:
-60 + 5q + 5q2 = 24q + 10q2 + q3 + (-27 + 2q)(6 + q)

Multiply (-27 + 2q) * (6 + q)
-60 + 5q + 5q2 = 24q + 10q2 + q3 + (-27(6 + q) + 2q * (6 + q))
-60 + 5q + 5q2 = 24q + 10q2 + q3 + ((6 * -27 + q * -27) + 2q * (6 + q))
-60 + 5q + 5q2 = 24q + 10q2 + q3 + ((-162 + -27q) + 2q * (6 + q))
-60 + 5q + 5q2 = 24q + 10q2 + q3 + (-162 + -27q + (6 * 2q + q * 2q))
-60 + 5q + 5q2 = 24q + 10q2 + q3 + (-162 + -27q + (12q + 2q2))

Combine like terms: -27q + 12q = -15q
-60 + 5q + 5q2 = 24q + 10q2 + q3 + (-162 + -15q + 2q2)

Reorder the terms:
-60 + 5q + 5q2 = -162 + 24q + -15q + 10q2 + 2q2 + q3

Combine like terms: 24q + -15q = 9q
-60 + 5q + 5q2 = -162 + 9q + 10q2 + 2q2 + q3

Combine like terms: 10q2 + 2q2 = 12q2
-60 + 5q + 5q2 = -162 + 9q + 12q2 + q3

Solving
-60 + 5q + 5q2 = -162 + 9q + 12q2 + q3

Solving for variable 'q'.

Reorder the terms:
-60 + 162 + 5q + -9q + 5q2 + -12q2 + -1q3 = -162 + 9q + 12q2 + q3 + 162 + -9q + -12q2 + -1q3

Combine like terms: -60 + 162 = 102
102 + 5q + -9q + 5q2 + -12q2 + -1q3 = -162 + 9q + 12q2 + q3 + 162 + -9q + -12q2 + -1q3

Combine like terms: 5q + -9q = -4q
102 + -4q + 5q2 + -12q2 + -1q3 = -162 + 9q + 12q2 + q3 + 162 + -9q + -12q2 + -1q3

Combine like terms: 5q2 + -12q2 = -7q2
102 + -4q + -7q2 + -1q3 = -162 + 9q + 12q2 + q3 + 162 + -9q + -12q2 + -1q3

Reorder the terms:
102 + -4q + -7q2 + -1q3 = -162 + 162 + 9q + -9q + 12q2 + -12q2 + q3 + -1q3

Combine like terms: -162 + 162 = 0
102 + -4q + -7q2 + -1q3 = 0 + 9q + -9q + 12q2 + -12q2 + q3 + -1q3
102 + -4q + -7q2 + -1q3 = 9q + -9q + 12q2 + -12q2 + q3 + -1q3

Combine like terms: 9q + -9q = 0
102 + -4q + -7q2 + -1q3 = 0 + 12q2 + -12q2 + q3 + -1q3
102 + -4q + -7q2 + -1q3 = 12q2 + -12q2 + q3 + -1q3

Combine like terms: 12q2 + -12q2 = 0
102 + -4q + -7q2 + -1q3 = 0 + q3 + -1q3
102 + -4q + -7q2 + -1q3 = q3 + -1q3

Combine like terms: q3 + -1q3 = 0
102 + -4q + -7q2 + -1q3 = 0

The solution to this equation could not be determined.

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