(5k-4)(5k-4)=36

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Solution for (5k-4)(5k-4)=36 equation: 


Simplifying
(5k + -4)(5k + -4) = 36

Reorder the terms:
(-4 + 5k)(5k + -4) = 36

Reorder the terms:
(-4 + 5k)(-4 + 5k) = 36

Multiply (-4 + 5k) * (-4 + 5k)
(-4(-4 + 5k) + 5k * (-4 + 5k)) = 36
((-4 * -4 + 5k * -4) + 5k * (-4 + 5k)) = 36
((16 + -20k) + 5k * (-4 + 5k)) = 36
(16 + -20k + (-4 * 5k + 5k * 5k)) = 36
(16 + -20k + (-20k + 25k2)) = 36

Combine like terms: -20k + -20k = -40k
(16 + -40k + 25k2) = 36

Solving
16 + -40k + 25k2 = 36

Solving for variable 'k'.

Reorder the terms:
16 + -36 + -40k + 25k2 = 36 + -36

Combine like terms: 16 + -36 = -20
-20 + -40k + 25k2 = 36 + -36

Combine like terms: 36 + -36 = 0
-20 + -40k + 25k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + -8k + 5k2) = 0

Factor a trinomial.
5((-2 + -5k)(2 + -1k)) = 0

Ignore the factor 5.

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 '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 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 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-0.4, 2}

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