2k^2+3k=35

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

Simplifying
2k2 + 3k = 35

Reorder the terms:
3k + 2k2 = 35

Solving
3k + 2k2 = 35

Solving for variable 'k'.

Reorder the terms:
-35 + 3k + 2k2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + 3k + 2k2 = 0

Factor a trinomial.
(-5 + -1k)(7 + -2k) = 0

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

Simplifying
-5 + -1k = 0

Solving
-5 + -1k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1k = 0 + 5
-1k = 0 + 5

Combine like terms: 0 + 5 = 5
-1k = 5

Divide each side by '-1'.
k = -5

Simplifying
k = -5
Subproblem 2
Set the factor '(7 + -2k)' equal to zero and attempt to solve:

Simplifying
7 + -2k = 0

Solving
7 + -2k = 0

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

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

Combine like terms: 7 + -7 = 0
0 + -2k = 0 + -7
-2k = 0 + -7

Combine like terms: 0 + -7 = -7
-2k = -7

Divide each side by '-2'.
k = 3.5

Simplifying
k = 3.5
Solution
k = {-5, 3.5}