(8k+7)(k+1)=9

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Solution for (8k+7)(k+1)=9 equation: 


Simplifying
(8k + 7)(k + 1) = 9

Reorder the terms:
(7 + 8k)(k + 1) = 9

Reorder the terms:
(7 + 8k)(1 + k) = 9

Multiply (7 + 8k) * (1 + k)
(7(1 + k) + 8k * (1 + k)) = 9
((1 * 7 + k * 7) + 8k * (1 + k)) = 9
((7 + 7k) + 8k * (1 + k)) = 9
(7 + 7k + (1 * 8k + k * 8k)) = 9
(7 + 7k + (8k + 8k2)) = 9

Combine like terms: 7k + 8k = 15k
(7 + 15k + 8k2) = 9

Solving
7 + 15k + 8k2 = 9

Solving for variable 'k'.

Reorder the terms:
7 + -9 + 15k + 8k2 = 9 + -9

Combine like terms: 7 + -9 = -2
-2 + 15k + 8k2 = 9 + -9

Combine like terms: 9 + -9 = 0
-2 + 15k + 8k2 = 0

Factor a trinomial.
(-2 + -1k)(1 + -8k) = 0


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

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1k = 0 + 2
-1k = 0 + 2

Combine like terms: 0 + 2 = 2
-1k = 2

Divide each side by '-1'.
k = -2

Simplifying
k = -2

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

Simplifying
1 + -8k = 0

Solving
1 + -8k = 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 + -8k = 0 + -1

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

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

Divide each side by '-8'.
k = 0.125

Simplifying
k = 0.125
Solution
k = {-2, 0.125}

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