(5k-2)(7k-4)=0

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Solution for (5k-2)(7k-4)=0 equation:


Simplifying
(5k + -2)(7k + -4) = 0

Reorder the terms:
(-2 + 5k)(7k + -4) = 0

Reorder the terms:
(-2 + 5k)(-4 + 7k) = 0

Multiply (-2 + 5k) * (-4 + 7k)
(-2(-4 + 7k) + 5k * (-4 + 7k)) = 0
((-4 * -2 + 7k * -2) + 5k * (-4 + 7k)) = 0
((8 + -14k) + 5k * (-4 + 7k)) = 0
(8 + -14k + (-4 * 5k + 7k * 5k)) = 0
(8 + -14k + (-20k + 35k2)) = 0

Combine like terms: -14k + -20k = -34k
(8 + -34k + 35k2) = 0

Solving
8 + -34k + 35k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(2 + -5k)(4 + -7k) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -7k)' equal to zero and attempt to solve: Simplifying 4 + -7k = 0 Solving 4 + -7k = 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 + -7k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7k = 0 + -4 -7k = 0 + -4 Combine like terms: 0 + -4 = -4 -7k = -4 Divide each side by '-7'. k = 0.5714285714 Simplifying k = 0.5714285714

Solution

k = {0.4, 0.5714285714}

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