7a^2-42a-49=0

Solution for 7a^2-42a-49=0 equation:

Simplifying
7a2 + -42a + -49 = 0

Reorder the terms:
-49 + -42a + 7a2 = 0

Solving
-49 + -42a + 7a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-7 + -6a + a2) = 0

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

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

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

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-1, 7}