14a^2+6=49a+6

Solution for 14a^2+6=49a+6 equation:

Simplifying
14a2 + 6 = 49a + 6

Reorder the terms:
6 + 14a2 = 49a + 6

Reorder the terms:
6 + 14a2 = 6 + 49a

Add '-6' to each side of the equation.
6 + -6 + 14a2 = 6 + -6 + 49a

Combine like terms: 6 + -6 = 0
0 + 14a2 = 6 + -6 + 49a
14a2 = 6 + -6 + 49a

Combine like terms: 6 + -6 = 0
14a2 = 0 + 49a
14a2 = 49a

Solving
14a2 = 49a

Solving for variable 'a'.

Reorder the terms:
-49a + 14a2 = 49a + -49a

Combine like terms: 49a + -49a = 0
-49a + 14a2 = 0

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

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-7 + 2a)' equal to zero and attempt to solve:

Simplifying
-7 + 2a = 0

Solving
-7 + 2a = 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 + 2a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2a = 0 + 7
2a = 0 + 7

Combine like terms: 0 + 7 = 7
2a = 7

Divide each side by '2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {0, 3.5}