35k^2=16k+3

Solution for 35k^2=16k+3 equation:

Simplifying
35k2 = 16k + 3

Reorder the terms:
35k2 = 3 + 16k

Solving
35k2 = 3 + 16k

Solving for variable 'k'.

Reorder the terms:
-3 + -16k + 35k2 = 3 + 16k + -3 + -16k

Reorder the terms:
-3 + -16k + 35k2 = 3 + -3 + 16k + -16k

Combine like terms: 3 + -3 = 0
-3 + -16k + 35k2 = 0 + 16k + -16k
-3 + -16k + 35k2 = 16k + -16k

Combine like terms: 16k + -16k = 0
-3 + -16k + 35k2 = 0

Factor a trinomial.
(-1 + -7k)(3 + -5k) = 0

Subproblem 1
Set the factor '(-1 + -7k)' equal to zero and attempt to solve:

Simplifying
-1 + -7k = 0

Solving
-1 + -7k = 0

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

Add '1' to each side of the equation.
-1 + 1 + -7k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7k = 0 + 1
-7k = 0 + 1

Combine like terms: 0 + 1 = 1
-7k = 1

Divide each side by '-7'.
k = -0.1428571429

Simplifying
k = -0.1428571429
Subproblem 2
Set the factor '(3 + -5k)' equal to zero and attempt to solve:

Simplifying
3 + -5k = 0

Solving
3 + -5k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5k = 0 + -3
-5k = 0 + -3

Combine like terms: 0 + -3 = -3
-5k = -3

Divide each side by '-5'.
k = 0.6

Simplifying
k = 0.6
Solution
k = {-0.1428571429, 0.6}