64-(k-7)(k-7)=0

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Solution for 64-(k-7)(k-7)=0 equation: 


Simplifying
64 + -1(k + -7)(k + -7) = 0

Reorder the terms:
64 + -1(-7 + k)(k + -7) = 0

Reorder the terms:
64 + -1(-7 + k)(-7 + k) = 0

Multiply (-7 + k) * (-7 + k)
64 + -1(-7(-7 + k) + k(-7 + k)) = 0
64 + -1((-7 * -7 + k * -7) + k(-7 + k)) = 0
64 + -1((49 + -7k) + k(-7 + k)) = 0
64 + -1(49 + -7k + (-7 * k + k * k)) = 0
64 + -1(49 + -7k + (-7k + k2)) = 0

Combine like terms: -7k + -7k = -14k
64 + -1(49 + -14k + k2) = 0
64 + (49 * -1 + -14k * -1 + k2 * -1) = 0
64 + (-49 + 14k + -1k2) = 0

Combine like terms: 64 + -49 = 15
15 + 14k + -1k2 = 0

Solving
15 + 14k + -1k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(15 + -1k)(1 + k) = 0


Subproblem 1
Set the factor '(15 + -1k)' equal to zero and attempt to solve:

Simplifying
15 + -1k = 0

Solving
15 + -1k = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1k = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1k = 0 + -15
-1k = 0 + -15

Combine like terms: 0 + -15 = -15
-1k = -15

Divide each side by '-1'.
k = 15

Simplifying
k = 15

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

Simplifying
1 + k = 0

Solving
1 + k = 0

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

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

Combine like terms: 1 + -1 = 0
0 + k = 0 + -1
k = 0 + -1

Combine like terms: 0 + -1 = -1
k = -1

Simplifying
k = -1
Solution
k = {15, -1}

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