4a^2=9a+9

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

Simplifying
4a2 = 9a + 9

Reorder the terms:
4a2 = 9 + 9a

Solving
4a2 = 9 + 9a

Solving for variable 'a'.

Reorder the terms:
-9 + -9a + 4a2 = 9 + 9a + -9 + -9a

Reorder the terms:
-9 + -9a + 4a2 = 9 + -9 + 9a + -9a

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

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

Factor a trinomial.
(-3 + -4a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-3 + -4a)' equal to zero and attempt to solve:

Simplifying
-3 + -4a = 0

Solving
-3 + -4a = 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 + -4a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4a = 0 + 3
-4a = 0 + 3

Combine like terms: 0 + 3 = 3
-4a = 3

Divide each side by '-4'.
a = -0.75

Simplifying
a = -0.75
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.75, 3}