(5k-8)(2k+5)=0

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Solution for (5k-8)(2k+5)=0 equation:


Simplifying
(5k + -8)(2k + 5) = 0

Reorder the terms:
(-8 + 5k)(2k + 5) = 0

Reorder the terms:
(-8 + 5k)(5 + 2k) = 0

Multiply (-8 + 5k) * (5 + 2k)
(-8(5 + 2k) + 5k * (5 + 2k)) = 0
((5 * -8 + 2k * -8) + 5k * (5 + 2k)) = 0
((-40 + -16k) + 5k * (5 + 2k)) = 0
(-40 + -16k + (5 * 5k + 2k * 5k)) = 0
(-40 + -16k + (25k + 10k2)) = 0

Combine like terms: -16k + 25k = 9k
(-40 + 9k + 10k2) = 0

Solving
-40 + 9k + 10k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-5 + -2k)(8 + -5k) = 0

Subproblem 1

Set the factor '(-5 + -2k)' equal to zero and attempt to solve: Simplifying -5 + -2k = 0 Solving -5 + -2k = 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 + -2k = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2k = 0 + 5 -2k = 0 + 5 Combine like terms: 0 + 5 = 5 -2k = 5 Divide each side by '-2'. k = -2.5 Simplifying k = -2.5

Subproblem 2

Set the factor '(8 + -5k)' equal to zero and attempt to solve: Simplifying 8 + -5k = 0 Solving 8 + -5k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5k = 0 + -8 -5k = 0 + -8 Combine like terms: 0 + -8 = -8 -5k = -8 Divide each side by '-5'. k = 1.6 Simplifying k = 1.6

Solution

k = {-2.5, 1.6}

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