5a^2-28a-45=-6a+3

Solution for 5a^2-28a-45=-6a+3 equation:

Simplifying
5a2 + -28a + -45 = -6a + 3

Reorder the terms:
-45 + -28a + 5a2 = -6a + 3

Reorder the terms:
-45 + -28a + 5a2 = 3 + -6a

Solving
-45 + -28a + 5a2 = 3 + -6a

Solving for variable 'a'.

Reorder the terms:
-45 + -3 + -28a + 6a + 5a2 = 3 + -6a + -3 + 6a

Combine like terms: -45 + -3 = -48
-48 + -28a + 6a + 5a2 = 3 + -6a + -3 + 6a

Combine like terms: -28a + 6a = -22a
-48 + -22a + 5a2 = 3 + -6a + -3 + 6a

Reorder the terms:
-48 + -22a + 5a2 = 3 + -3 + -6a + 6a

Combine like terms: 3 + -3 = 0
-48 + -22a + 5a2 = 0 + -6a + 6a
-48 + -22a + 5a2 = -6a + 6a

Combine like terms: -6a + 6a = 0
-48 + -22a + 5a2 = 0

Factor a trinomial.
(-8 + -5a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-8 + -5a)' equal to zero and attempt to solve:

Simplifying
-8 + -5a = 0

Solving
-8 + -5a = 0

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

Add '8' to each side of the equation.
-8 + 8 + -5a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5a = 0 + 8
-5a = 0 + 8

Combine like terms: 0 + 8 = 8
-5a = 8

Divide each side by '-5'.
a = -1.6

Simplifying
a = -1.6
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 = {-1.6, 6}