a^2+4a+4=25-11a^2

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Solution for a^2+4a+4=25-11a^2 equation: 


Simplifying
a2 + 4a + 4 = 25 + -11a2

Reorder the terms:
4 + 4a + a2 = 25 + -11a2

Solving
4 + 4a + a2 = 25 + -11a2

Solving for variable 'a'.

Reorder the terms:
4 + -25 + 4a + a2 + 11a2 = 25 + -11a2 + -25 + 11a2

Combine like terms: 4 + -25 = -21
-21 + 4a + a2 + 11a2 = 25 + -11a2 + -25 + 11a2

Combine like terms: a2 + 11a2 = 12a2
-21 + 4a + 12a2 = 25 + -11a2 + -25 + 11a2

Reorder the terms:
-21 + 4a + 12a2 = 25 + -25 + -11a2 + 11a2

Combine like terms: 25 + -25 = 0
-21 + 4a + 12a2 = 0 + -11a2 + 11a2
-21 + 4a + 12a2 = -11a2 + 11a2

Combine like terms: -11a2 + 11a2 = 0
-21 + 4a + 12a2 = 0

Factor a trinomial.
(-3 + -2a)(7 + -6a) = 0


Subproblem 1
Set the factor '(-3 + -2a)' equal to zero and attempt to solve:

Simplifying
-3 + -2a = 0

Solving
-3 + -2a = 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 + -2a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2a = 0 + 3
-2a = 0 + 3

Combine like terms: 0 + 3 = 3
-2a = 3

Divide each side by '-2'.
a = -1.5

Simplifying
a = -1.5

Subproblem 2
Set the factor '(7 + -6a)' equal to zero and attempt to solve:

Simplifying
7 + -6a = 0

Solving
7 + -6a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6a = 0 + -7

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

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

Divide each side by '-6'.
a = 1.166666667

Simplifying
a = 1.166666667
Solution
a = {-1.5, 1.166666667}

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