7a^2-52a+21=0

Solution for 7a^2-52a+21=0 equation:

Simplifying
7a2 + -52a + 21 = 0

Reorder the terms:
21 + -52a + 7a2 = 0

Solving
21 + -52a + 7a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(3 + -7a)' equal to zero and attempt to solve:

Simplifying
3 + -7a = 0

Solving
3 + -7a = 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 + -7a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7a = 0 + -3
-7a = 0 + -3

Combine like terms: 0 + -3 = -3
-7a = -3

Divide each side by '-7'.
a = 0.4285714286

Simplifying
a = 0.4285714286
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 = {0.4285714286, 7}