4a^2-45=-3a

Solution for 4a^2-45=-3a equation:

Simplifying
4a2 + -45 = -3a

Reorder the terms:
-45 + 4a2 = -3a

Solving
-45 + 4a2 = -3a

Solving for variable 'a'.

Reorder the terms:
-45 + 3a + 4a2 = -3a + 3a

Combine like terms: -3a + 3a = 0
-45 + 3a + 4a2 = 0

Factor a trinomial.
(-15 + -4a)(3 + -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 '(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 = {-3.75, 3}