3a^2-10a=48

Solution for 3a^2-10a=48 equation:

Simplifying
3a2 + -10a = 48

Reorder the terms:
-10a + 3a2 = 48

Solving
-10a + 3a2 = 48

Solving for variable 'a'.

Reorder the terms:
-48 + -10a + 3a2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + -10a + 3a2 = 0

Factor a trinomial.
(-8 + -3a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-8 + -3a)' equal to zero and attempt to solve:

Simplifying
-8 + -3a = 0

Solving
-8 + -3a = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3a = 0 + 8
-3a = 0 + 8

Combine like terms: 0 + 8 = 8
-3a = 8

Divide each side by '-3'.
a = -2.666666667

Simplifying
a = -2.666666667
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-2.666666667, 6}