4a^2+9a-4=5

Solution for 4a^2+9a-4=5 equation:

Simplifying
4a2 + 9a + -4 = 5

Reorder the terms:
-4 + 9a + 4a2 = 5

Solving
-4 + 9a + 4a2 = 5

Solving for variable 'a'.

Reorder the terms:
-4 + -5 + 9a + 4a2 = 5 + -5

Combine like terms: -4 + -5 = -9
-9 + 9a + 4a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-9 + 9a + 4a2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-3, 0.75}