3a^2-14a-10=14

Solution for 3a^2-14a-10=14 equation:

Simplifying
3a2 + -14a + -10 = 14

Reorder the terms:
-10 + -14a + 3a2 = 14

Solving
-10 + -14a + 3a2 = 14

Solving for variable 'a'.

Reorder the terms:
-10 + -14 + -14a + 3a2 = 14 + -14

Combine like terms: -10 + -14 = -24
-24 + -14a + 3a2 = 14 + -14

Combine like terms: 14 + -14 = 0
-24 + -14a + 3a2 = 0

Factor a trinomial.
(-4 + -3a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-4 + -3a)' equal to zero and attempt to solve:

Simplifying
-4 + -3a = 0

Solving
-4 + -3a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3a = 0 + 4
-3a = 0 + 4

Combine like terms: 0 + 4 = 4
-3a = 4

Divide each side by '-3'.
a = -1.333333333

Simplifying
a = -1.333333333
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 = {-1.333333333, 6}