(k-10)(4k+9)=0

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Solution for (k-10)(4k+9)=0 equation: 


Simplifying
(k + -10)(4k + 9) = 0

Reorder the terms:
(-10 + k)(4k + 9) = 0

Reorder the terms:
(-10 + k)(9 + 4k) = 0

Multiply (-10 + k) * (9 + 4k)
(-10(9 + 4k) + k(9 + 4k)) = 0
((9 * -10 + 4k * -10) + k(9 + 4k)) = 0
((-90 + -40k) + k(9 + 4k)) = 0
(-90 + -40k + (9 * k + 4k * k)) = 0
(-90 + -40k + (9k + 4k2)) = 0

Combine like terms: -40k + 9k = -31k
(-90 + -31k + 4k2) = 0

Solving
-90 + -31k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-9 + -4k)(10 + -1k) = 0


Subproblem 1
Set the factor '(-9 + -4k)' equal to zero and attempt to solve:

Simplifying
-9 + -4k = 0

Solving
-9 + -4k = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4k = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4k = 0 + 9
-4k = 0 + 9

Combine like terms: 0 + 9 = 9
-4k = 9

Divide each side by '-4'.
k = -2.25

Simplifying
k = -2.25

Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve:

Simplifying
10 + -1k = 0

Solving
10 + -1k = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1k = 0 + -10
-1k = 0 + -10

Combine like terms: 0 + -10 = -10
-1k = -10

Divide each side by '-1'.
k = 10

Simplifying
k = 10
Solution
k = {-2.25, 10}

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