0=-7a^2-42+49a

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

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

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

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

Solving for variable 'a'.

Combine like terms: 0 + 42 = 42
42 + -49a + 7a2 = -42 + 49a + -7a2 + 42 + -49a + 7a2

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

Combine like terms: -42 + 42 = 0
42 + -49a + 7a2 = 0 + 49a + -49a + -7a2 + 7a2
42 + -49a + 7a2 = 49a + -49a + -7a2 + 7a2

Combine like terms: 49a + -49a = 0
42 + -49a + 7a2 = 0 + -7a2 + 7a2
42 + -49a + 7a2 = -7a2 + 7a2

Combine like terms: -7a2 + 7a2 = 0
42 + -49a + 7a2 = 0

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

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