4x^2-4kx-35k^2=0

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Solution for 4x^2-4kx-35k^2=0 equation: 


Simplifying
4x2 + -4kx + -35k2 = 0

Reorder the terms:
-4kx + -35k2 + 4x2 = 0

Solving
-4kx + -35k2 + 4x2 = 0

Solving for variable 'k'.

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


Subproblem 1
Set the factor '(-5k + -2x)' equal to zero and attempt to solve:

Simplifying
-5k + -2x = 0

Solving
-5k + -2x = 0

Move all terms containing k to the left, all other terms to the right.

Add '2x' to each side of the equation.
-5k + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
-5k + 0 = 0 + 2x
-5k = 0 + 2x
Remove the zero:
-5k = 2x

Divide each side by '-5'.
k = -0.4x

Simplifying
k = -0.4x

Subproblem 2
Set the factor '(7k + -2x)' equal to zero and attempt to solve:

Simplifying
7k + -2x = 0

Solving
7k + -2x = 0

Move all terms containing k to the left, all other terms to the right.

Add '2x' to each side of the equation.
7k + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
7k + 0 = 0 + 2x
7k = 0 + 2x
Remove the zero:
7k = 2x

Divide each side by '7'.
k = 0.2857142857x

Simplifying
k = 0.2857142857x
Solution
k = {-0.4x, 0.2857142857x}

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