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((-6 + -1a)(1 + -1a)) = 0

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
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
Solution
a = {-6, 1}