(3k+4)(6k+5)=0

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Solution for (3k+4)(6k+5)=0 equation:


Simplifying
(3k + 4)(6k + 5) = 0

Reorder the terms:
(4 + 3k)(6k + 5) = 0

Reorder the terms:
(4 + 3k)(5 + 6k) = 0

Multiply (4 + 3k) * (5 + 6k)
(4(5 + 6k) + 3k * (5 + 6k)) = 0
((5 * 4 + 6k * 4) + 3k * (5 + 6k)) = 0
((20 + 24k) + 3k * (5 + 6k)) = 0
(20 + 24k + (5 * 3k + 6k * 3k)) = 0
(20 + 24k + (15k + 18k2)) = 0

Combine like terms: 24k + 15k = 39k
(20 + 39k + 18k2) = 0

Solving
20 + 39k + 18k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(4 + 3k)(5 + 6k) = 0

Subproblem 1

Set the factor '(4 + 3k)' equal to zero and attempt to solve: Simplifying 4 + 3k = 0 Solving 4 + 3k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3k = 0 + -4 3k = 0 + -4 Combine like terms: 0 + -4 = -4 3k = -4 Divide each side by '3'. k = -1.333333333 Simplifying k = -1.333333333

Subproblem 2

Set the factor '(5 + 6k)' equal to zero and attempt to solve: Simplifying 5 + 6k = 0 Solving 5 + 6k = 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 + 6k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6k = 0 + -5 6k = 0 + -5 Combine like terms: 0 + -5 = -5 6k = -5 Divide each side by '6'. k = -0.8333333333 Simplifying k = -0.8333333333

Solution

k = {-1.333333333, -0.8333333333}

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