(5X)(3X+6)=45

Solution for (5X)(3X+6)=45 equation:

Simplifying
(5X)(3X + 6) = 45

Remove parenthesis around (5X)
5X(3X + 6) = 45

Reorder the terms:
5X(6 + 3X) = 45
(6 * 5X + 3X * 5X) = 45
(30X + 15X2) = 45

Solving
30X + 15X2 = 45

Solving for variable 'X'.

Reorder the terms:
-45 + 30X + 15X2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 30X + 15X2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-3 + 2X + X2) = 0

Factor a trinomial.
15((-3 + -1X)(1 + -1X)) = 0

Ignore the factor 15.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Solution
X = {-3, 1}