11a^2=4a^2+35+28a

Solution for 11a^2=4a^2+35+28a equation:

Simplifying
11a2 = 4a2 + 35 + 28a

Reorder the terms:
11a2 = 35 + 28a + 4a2

Solving
11a2 = 35 + 28a + 4a2

Solving for variable 'a'.

Reorder the terms:
-35 + -28a + 11a2 + -4a2 = 35 + 28a + 4a2 + -35 + -28a + -4a2

Combine like terms: 11a2 + -4a2 = 7a2
-35 + -28a + 7a2 = 35 + 28a + 4a2 + -35 + -28a + -4a2

Reorder the terms:
-35 + -28a + 7a2 = 35 + -35 + 28a + -28a + 4a2 + -4a2

Combine like terms: 35 + -35 = 0
-35 + -28a + 7a2 = 0 + 28a + -28a + 4a2 + -4a2
-35 + -28a + 7a2 = 28a + -28a + 4a2 + -4a2

Combine like terms: 28a + -28a = 0
-35 + -28a + 7a2 = 0 + 4a2 + -4a2
-35 + -28a + 7a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
-35 + -28a + 7a2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-5 + -4a + a2) = 0

Factor a trinomial.
7((-1 + -1a)(5 + -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 '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-1, 5}