(5k+2)(2k-3)=

Solution for (5k+2)(2k-3)= equation:

Simplifying
(5k + 2)(2k + -3) = 0

Reorder the terms:
(2 + 5k)(2k + -3) = 0

Reorder the terms:
(2 + 5k)(-3 + 2k) = 0

Multiply (2 + 5k) * (-3 + 2k)
(2(-3 + 2k) + 5k * (-3 + 2k)) = 0
((-3 * 2 + 2k * 2) + 5k * (-3 + 2k)) = 0
((-6 + 4k) + 5k * (-3 + 2k)) = 0
(-6 + 4k + (-3 * 5k + 2k * 5k)) = 0
(-6 + 4k + (-15k + 10k2)) = 0

Combine like terms: 4k + -15k = -11k
(-6 + -11k + 10k2) = 0

Solving
-6 + -11k + 10k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-2 + -5k)(3 + -2k) = 0

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 '(3 + -2k)' equal to zero and attempt to solve:

Simplifying
3 + -2k = 0

Solving
3 + -2k = 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 + -2k = 0 + -3

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

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

Divide each side by '-2'.
k = 1.5

Simplifying
k = 1.5
Solution
k = {-0.4, 1.5}