7a^2-14a-62=-6

Solution for 7a^2-14a-62=-6 equation:

Simplifying
7a2 + -14a + -62 = -6

Reorder the terms:
-62 + -14a + 7a2 = -6

Solving
-62 + -14a + 7a2 = -6

Solving for variable 'a'.

Reorder the terms:
-62 + 6 + -14a + 7a2 = -6 + 6

Combine like terms: -62 + 6 = -56
-56 + -14a + 7a2 = -6 + 6

Combine like terms: -6 + 6 = 0
-56 + -14a + 7a2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + -2a + a2) = 0

Factor a trinomial.
7((-2 + -1a)(4 + -1a)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-2 + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 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 + -1a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1a = 0 + 2
-1a = 0 + 2

Combine like terms: 0 + 2 = 2
-1a = 2

Divide each side by '-1'.
a = -2

Simplifying
a = -2
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 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 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-2, 4}