7a^2-56a+84=0

Solution for 7a^2-56a+84=0 equation:

Simplifying
7a2 + -56a + 84 = 0

Reorder the terms:
84 + -56a + 7a2 = 0

Solving
84 + -56a + 7a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7'.
7(12 + -8a + a2) = 0

Factor a trinomial.
7((2 + -1a)(6 + -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 '(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 = {2, 6}