5a^2-6=-7a

Solution for 5a^2-6=-7a equation:

Simplifying
5a2 + -6 = -7a

Reorder the terms:
-6 + 5a2 = -7a

Solving
-6 + 5a2 = -7a

Solving for variable 'a'.

Reorder the terms:
-6 + 7a + 5a2 = -7a + 7a

Combine like terms: -7a + 7a = 0
-6 + 7a + 5a2 = 0

Factor a trinomial.
(-2 + -1a)(3 + -5a) = 0

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 + -5a)' equal to zero and attempt to solve:

Simplifying
3 + -5a = 0

Solving
3 + -5a = 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 + -5a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5a = 0 + -3
-5a = 0 + -3

Combine like terms: 0 + -3 = -3
-5a = -3

Divide each side by '-5'.
a = 0.6

Simplifying
a = 0.6
Solution
a = {-2, 0.6}