5x(x-3)-2(x-3)=

Solution for 5x(x-3)-2(x-3)= equation:

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

Reorder the terms:
5x(-3 + x) + -2(x + -3) = 0
(-3 * 5x + x * 5x) + -2(x + -3) = 0
(-15x + 5x2) + -2(x + -3) = 0

Reorder the terms:
-15x + 5x2 + -2(-3 + x) = 0
-15x + 5x2 + (-3 * -2 + x * -2) = 0
-15x + 5x2 + (6 + -2x) = 0

Reorder the terms:
6 + -15x + -2x + 5x2 = 0

Combine like terms: -15x + -2x = -17x
6 + -17x + 5x2 = 0

Solving
6 + -17x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -5x)(3 + -1x) = 0

Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.4, 3}