7a^2=42+7a

Solution for 7a^2=42+7a equation:

Simplifying
7a2 = 42 + 7a

Solving
7a2 = 42 + 7a

Solving for variable 'a'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + -1a + a2) = 0

Factor a trinomial.
7((-2 + -1a)(3 + -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 '(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 = {-2, 3}