7a^2-6=11a

Solution for 7a^2-6=11a equation:

Simplifying
7a2 + -6 = 11a

Reorder the terms:
-6 + 7a2 = 11a

Solving
-6 + 7a2 = 11a

Solving for variable 'a'.

Reorder the terms:
-6 + -11a + 7a2 = 11a + -11a

Combine like terms: 11a + -11a = 0
-6 + -11a + 7a2 = 0

Factor a trinomial.
(-3 + -7a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-3 + -7a)' equal to zero and attempt to solve:

Simplifying
-3 + -7a = 0

Solving
-3 + -7a = 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 + -7a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7a = 0 + 3
-7a = 0 + 3

Combine like terms: 0 + 3 = 3
-7a = 3

Divide each side by '-7'.
a = -0.4285714286

Simplifying
a = -0.4285714286
Subproblem 2
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
Solution
a = {-0.4285714286, 2}