4a^2-9a=90

Solution for 4a^2-9a=90 equation:

Simplifying
4a2 + -9a = 90

Reorder the terms:
-9a + 4a2 = 90

Solving
-9a + 4a2 = 90

Solving for variable 'a'.

Reorder the terms:
-90 + -9a + 4a2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -9a + 4a2 = 0

Factor a trinomial.
(-15 + -4a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-15 + -4a)' equal to zero and attempt to solve:

Simplifying
-15 + -4a = 0

Solving
-15 + -4a = 0

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

Add '15' to each side of the equation.
-15 + 15 + -4a = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4a = 0 + 15
-4a = 0 + 15

Combine like terms: 0 + 15 = 15
-4a = 15

Divide each side by '-4'.
a = -3.75

Simplifying
a = -3.75
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-3.75, 6}