(5k+7)(k+5)=23

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Solution for (5k+7)(k+5)=23 equation:


Simplifying
(5k + 7)(k + 5) = 23

Reorder the terms:
(7 + 5k)(k + 5) = 23

Reorder the terms:
(7 + 5k)(5 + k) = 23

Multiply (7 + 5k) * (5 + k)
(7(5 + k) + 5k * (5 + k)) = 23
((5 * 7 + k * 7) + 5k * (5 + k)) = 23
((35 + 7k) + 5k * (5 + k)) = 23
(35 + 7k + (5 * 5k + k * 5k)) = 23
(35 + 7k + (25k + 5k2)) = 23

Combine like terms: 7k + 25k = 32k
(35 + 32k + 5k2) = 23

Solving
35 + 32k + 5k2 = 23

Solving for variable 'k'.

Reorder the terms:
35 + -23 + 32k + 5k2 = 23 + -23

Combine like terms: 35 + -23 = 12
12 + 32k + 5k2 = 23 + -23

Combine like terms: 23 + -23 = 0
12 + 32k + 5k2 = 0

Factor a trinomial.
(6 + k)(2 + 5k) = 0

Subproblem 1

Set the factor '(6 + k)' equal to zero and attempt to solve: Simplifying 6 + k = 0 Solving 6 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + k = 0 + -6 Combine like terms: 6 + -6 = 0 0 + k = 0 + -6 k = 0 + -6 Combine like terms: 0 + -6 = -6 k = -6 Simplifying k = -6

Subproblem 2

Set the factor '(2 + 5k)' equal to zero and attempt to solve: Simplifying 2 + 5k = 0 Solving 2 + 5k = 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 + 5k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5k = 0 + -2 5k = 0 + -2 Combine like terms: 0 + -2 = -2 5k = -2 Divide each side by '5'. k = -0.4 Simplifying k = -0.4

Solution

k = {-6, -0.4}

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