3(a-5)=6a(3a-15)

Solution for 3(a-5)=6a(3a-15) equation:

Simplifying
3(a + -5) = 6a(3a + -15)

Reorder the terms:
3(-5 + a) = 6a(3a + -15)
(-5 * 3 + a * 3) = 6a(3a + -15)
(-15 + 3a) = 6a(3a + -15)

Reorder the terms:
-15 + 3a = 6a(-15 + 3a)
-15 + 3a = (-15 * 6a + 3a * 6a)
-15 + 3a = (-90a + 18a2)

Solving
-15 + 3a = -90a + 18a2

Solving for variable 'a'.

Combine like terms: 3a + 90a = 93a
-15 + 93a + -18a2 = -90a + 18a2 + 90a + -18a2

Reorder the terms:
-15 + 93a + -18a2 = -90a + 90a + 18a2 + -18a2

Combine like terms: -90a + 90a = 0
-15 + 93a + -18a2 = 0 + 18a2 + -18a2
-15 + 93a + -18a2 = 18a2 + -18a2

Combine like terms: 18a2 + -18a2 = 0
-15 + 93a + -18a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 31a + -6a2) = 0

Factor a trinomial.
3((-5 + a)(1 + -6a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + a)' equal to zero and attempt to solve:

Simplifying
-5 + a = 0

Solving
-5 + a = 0

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

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

Combine like terms: -5 + 5 = 0
0 + a = 0 + 5
a = 0 + 5

Combine like terms: 0 + 5 = 5
a = 5

Simplifying
a = 5
Subproblem 2
Set the factor '(1 + -6a)' equal to zero and attempt to solve:

Simplifying
1 + -6a = 0

Solving
1 + -6a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6a = 0 + -1
-6a = 0 + -1

Combine like terms: 0 + -1 = -1
-6a = -1

Divide each side by '-6'.
a = 0.1666666667

Simplifying
a = 0.1666666667
Solution
a = {5, 0.1666666667}