(q+7)(q+7)+3=52

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Solution for (q+7)(q+7)+3=52 equation: 


Simplifying
(q + 7)(q + 7) + 3 = 52

Reorder the terms:
(7 + q)(q + 7) + 3 = 52

Reorder the terms:
(7 + q)(7 + q) + 3 = 52

Multiply (7 + q) * (7 + q)
(7(7 + q) + q(7 + q)) + 3 = 52
((7 * 7 + q * 7) + q(7 + q)) + 3 = 52
((49 + 7q) + q(7 + q)) + 3 = 52
(49 + 7q + (7 * q + q * q)) + 3 = 52
(49 + 7q + (7q + q2)) + 3 = 52

Combine like terms: 7q + 7q = 14q
(49 + 14q + q2) + 3 = 52

Reorder the terms:
49 + 3 + 14q + q2 = 52

Combine like terms: 49 + 3 = 52
52 + 14q + q2 = 52

Add '-52' to each side of the equation.
52 + 14q + -52 + q2 = 52 + -52

Reorder the terms:
52 + -52 + 14q + q2 = 52 + -52

Combine like terms: 52 + -52 = 0
0 + 14q + q2 = 52 + -52
14q + q2 = 52 + -52

Combine like terms: 52 + -52 = 0
14q + q2 = 0

Solving
14q + q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), 'q'.
q(14 + q) = 0


Subproblem 1
Set the factor 'q' equal to zero and attempt to solve:

Simplifying
q = 0

Solving
q = 0

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

Simplifying
q = 0

Subproblem 2
Set the factor '(14 + q)' equal to zero and attempt to solve:

Simplifying
14 + q = 0

Solving
14 + q = 0

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

Add '-14' to each side of the equation.
14 + -14 + q = 0 + -14

Combine like terms: 14 + -14 = 0
0 + q = 0 + -14
q = 0 + -14

Combine like terms: 0 + -14 = -14
q = -14

Simplifying
q = -14
Solution
q = {0, -14}

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