3a^2-16a-7=5

Solution for 3a^2-16a-7=5 equation:

Simplifying
3a2 + -16a + -7 = 5

Reorder the terms:
-7 + -16a + 3a2 = 5

Solving
-7 + -16a + 3a2 = 5

Solving for variable 'a'.

Reorder the terms:
-7 + -5 + -16a + 3a2 = 5 + -5

Combine like terms: -7 + -5 = -12
-12 + -16a + 3a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-12 + -16a + 3a2 = 0

Factor a trinomial.
(-2 + -3a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-2 + -3a)' equal to zero and attempt to solve:

Simplifying
-2 + -3a = 0

Solving
-2 + -3a = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3a = 0 + 2
-3a = 0 + 2

Combine like terms: 0 + 2 = 2
-3a = 2

Divide each side by '-3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
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 = {-0.6666666667, 6}