5(k+5)(5k+3)=0

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Solution for 5(k+5)(5k+3)=0 equation:


Simplifying
5(k + 5)(5k + 3) = 0

Reorder the terms:
5(5 + k)(5k + 3) = 0

Reorder the terms:
5(5 + k)(3 + 5k) = 0

Multiply (5 + k) * (3 + 5k)
5(5(3 + 5k) + k(3 + 5k)) = 0
5((3 * 5 + 5k * 5) + k(3 + 5k)) = 0
5((15 + 25k) + k(3 + 5k)) = 0
5(15 + 25k + (3 * k + 5k * k)) = 0
5(15 + 25k + (3k + 5k2)) = 0

Combine like terms: 25k + 3k = 28k
5(15 + 28k + 5k2) = 0
(15 * 5 + 28k * 5 + 5k2 * 5) = 0
(75 + 140k + 25k2) = 0

Solving
75 + 140k + 25k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '5'.
5(15 + 28k + 5k2) = 0

Factor a trinomial.
5((5 + k)(3 + 5k)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(5 + k)' equal to zero and attempt to solve: Simplifying 5 + k = 0 Solving 5 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + k = 0 + -5 k = 0 + -5 Combine like terms: 0 + -5 = -5 k = -5 Simplifying k = -5

Subproblem 2

Set the factor '(3 + 5k)' equal to zero and attempt to solve: Simplifying 3 + 5k = 0 Solving 3 + 5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5k = 0 + -3 5k = 0 + -3 Combine like terms: 0 + -3 = -3 5k = -3 Divide each side by '5'. k = -0.6 Simplifying k = -0.6

Solution

k = {-5, -0.6}

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