7a^2-42=35a

Solution for 7a^2-42=35a equation:

Simplifying
7a2 + -42 = 35a

Reorder the terms:
-42 + 7a2 = 35a

Solving
-42 + 7a2 = 35a

Solving for variable 'a'.

Reorder the terms:
-42 + -35a + 7a2 = 35a + -35a

Combine like terms: 35a + -35a = 0
-42 + -35a + 7a2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + -5a + 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}