5a^2+46a+53=5

Solution for 5a^2+46a+53=5 equation:

Simplifying
5a2 + 46a + 53 = 5

Reorder the terms:
53 + 46a + 5a2 = 5

Solving
53 + 46a + 5a2 = 5

Solving for variable 'a'.

Reorder the terms:
53 + -5 + 46a + 5a2 = 5 + -5

Combine like terms: 53 + -5 = 48
48 + 46a + 5a2 = 5 + -5

Combine like terms: 5 + -5 = 0
48 + 46a + 5a2 = 0

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

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

Simplifying
8 + a = 0

Solving
8 + a = 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 + a = 0 + -8

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

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

Simplifying
a = -8
Subproblem 2
Set the factor '(6 + 5a)' equal to zero and attempt to solve:

Simplifying
6 + 5a = 0

Solving
6 + 5a = 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 + 5a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5a = 0 + -6
5a = 0 + -6

Combine like terms: 0 + -6 = -6
5a = -6

Divide each side by '5'.
a = -1.2

Simplifying
a = -1.2
Solution
a = {-8, -1.2}