(q-8)(q-7)=0

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Solution for (q-8)(q-7)=0 equation: 


Simplifying
(q + -8)(q + -7) = 0

Reorder the terms:
(-8 + q)(q + -7) = 0

Reorder the terms:
(-8 + q)(-7 + q) = 0

Multiply (-8 + q) * (-7 + q)
(-8(-7 + q) + q(-7 + q)) = 0
((-7 * -8 + q * -8) + q(-7 + q)) = 0
((56 + -8q) + q(-7 + q)) = 0
(56 + -8q + (-7 * q + q * q)) = 0
(56 + -8q + (-7q + q2)) = 0

Combine like terms: -8q + -7q = -15q
(56 + -15q + q2) = 0

Solving
56 + -15q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(7 + -1q)(8 + -1q) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1q)' equal to zero and attempt to solve:

Simplifying
8 + -1q = 0

Solving
8 + -1q = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1q = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1q = 0 + -8
-1q = 0 + -8

Combine like terms: 0 + -8 = -8
-1q = -8

Divide each side by '-1'.
q = 8

Simplifying
q = 8
Solution
q = {7, 8}

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