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Simplifying
(5k + 8l)(5k + -8l) = 0
Multiply (5k + 8l) * (5k + -8l)
(5k * (5k + -8l) + 8l * (5k + -8l)) = 0
((5k * 5k + -8l * 5k) + 8l * (5k + -8l)) = 0
Reorder the terms:
((-40kl + 25k2) + 8l * (5k + -8l)) = 0
((-40kl + 25k2) + 8l * (5k + -8l)) = 0
(-40kl + 25k2 + (5k * 8l + -8l * 8l)) = 0
(-40kl + 25k2 + (40kl + -64l2)) = 0
Reorder the terms:
(-40kl + 40kl + 25k2 + -64l2) = 0
Combine like terms: -40kl + 40kl = 0
(0 + 25k2 + -64l2) = 0
(25k2 + -64l2) = 0
Solving
25k2 + -64l2 = 0
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '64l2' to each side of the equation.
25k2 + -64l2 + 64l2 = 0 + 64l2
Combine like terms: -64l2 + 64l2 = 0
25k2 + 0 = 0 + 64l2
25k2 = 0 + 64l2
Remove the zero:
25k2 = 64l2
Divide each side by '25'.
k2 = 2.56l2
Simplifying
k2 = 2.56l2
Take the square root of each side:
k = {-1.6l, 1.6l}
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