3a^2-6a-52=-7

Solution for 3a^2-6a-52=-7 equation:

Simplifying
3a2 + -6a + -52 = -7

Reorder the terms:
-52 + -6a + 3a2 = -7

Solving
-52 + -6a + 3a2 = -7

Solving for variable 'a'.

Reorder the terms:
-52 + 7 + -6a + 3a2 = -7 + 7

Combine like terms: -52 + 7 = -45
-45 + -6a + 3a2 = -7 + 7

Combine like terms: -7 + 7 = 0
-45 + -6a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2a + a2) = 0

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

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

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 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 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-3, 5}