a^2+4a+9=3a^2+4a+1

Solution for a^2+4a+9=3a^2+4a+1 equation:

Simplifying
a2 + 4a + 9 = 3a2 + 4a + 1

Reorder the terms:
9 + 4a + a2 = 3a2 + 4a + 1

Reorder the terms:
9 + 4a + a2 = 1 + 4a + 3a2

Add '-4a' to each side of the equation.
9 + 4a + -4a + a2 = 1 + 4a + -4a + 3a2

Combine like terms: 4a + -4a = 0
9 + 0 + a2 = 1 + 4a + -4a + 3a2
9 + a2 = 1 + 4a + -4a + 3a2

Combine like terms: 4a + -4a = 0
9 + a2 = 1 + 0 + 3a2
9 + a2 = 1 + 3a2

Solving
9 + a2 = 1 + 3a2

Solving for variable 'a'.

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

Add '-3a2' to each side of the equation.
9 + a2 + -3a2 = 1 + 3a2 + -3a2

Combine like terms: a2 + -3a2 = -2a2
9 + -2a2 = 1 + 3a2 + -3a2

Combine like terms: 3a2 + -3a2 = 0
9 + -2a2 = 1 + 0
9 + -2a2 = 1

Add '-9' to each side of the equation.
9 + -9 + -2a2 = 1 + -9

Combine like terms: 9 + -9 = 0
0 + -2a2 = 1 + -9
-2a2 = 1 + -9

Combine like terms: 1 + -9 = -8
-2a2 = -8

Divide each side by '-2'.
a2 = 4

Simplifying
a2 = 4

Take the square root of each side:
a = {-2, 2}