7a^2+49a-210=0

Solution for 7a^2+49a-210=0 equation:

Simplifying
7a2 + 49a + -210 = 0

Reorder the terms:
-210 + 49a + 7a2 = 0

Solving
-210 + 49a + 7a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-30 + 7a + a2) = 0

Factor a trinomial.
7((-10 + -1a)(3 + -1a)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-10 + -1a)' equal to zero and attempt to solve:

Simplifying
-10 + -1a = 0

Solving
-10 + -1a = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1a = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1a = 0 + 10
-1a = 0 + 10

Combine like terms: 0 + 10 = 10
-1a = 10

Divide each side by '-1'.
a = -10

Simplifying
a = -10
Subproblem 2
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
Solution
a = {-10, 3}