452=-q^2-2q+515

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Solution for 452=-q^2-2q+515 equation: 


Simplifying
452 = -1q2 + -2q + 515

Reorder the terms:
452 = 515 + -2q + -1q2

Solving
452 = 515 + -2q + -1q2

Solving for variable 'q'.

Combine like terms: 452 + -515 = -63
-63 + 2q + q2 = 515 + -2q + -1q2 + -515 + 2q + q2

Reorder the terms:
-63 + 2q + q2 = 515 + -515 + -2q + 2q + -1q2 + q2

Combine like terms: 515 + -515 = 0
-63 + 2q + q2 = 0 + -2q + 2q + -1q2 + q2
-63 + 2q + q2 = -2q + 2q + -1q2 + q2

Combine like terms: -2q + 2q = 0
-63 + 2q + q2 = 0 + -1q2 + q2
-63 + 2q + q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
-63 + 2q + q2 = 0

Factor a trinomial.
(-9 + -1q)(7 + -1q) = 0


Subproblem 1
Set the factor '(-9 + -1q)' equal to zero and attempt to solve:

Simplifying
-9 + -1q = 0

Solving
-9 + -1q = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1q = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1q = 0 + 9
-1q = 0 + 9

Combine like terms: 0 + 9 = 9
-1q = 9

Divide each side by '-1'.
q = -9

Simplifying
q = -9

Subproblem 2
Set the factor '(7 + -1q)' equal to zero and attempt to solve:

Simplifying
7 + -1q = 0

Solving
7 + -1q = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1q = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1q = 0 + -7
-1q = 0 + -7

Combine like terms: 0 + -7 = -7
-1q = -7

Divide each side by '-1'.
q = 7

Simplifying
q = 7
Solution
q = {-9, 7}

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