3a^2+5a-13=-5

Solution for 3a^2+5a-13=-5 equation:

Simplifying
3a2 + 5a + -13 = -5

Reorder the terms:
-13 + 5a + 3a2 = -5

Solving
-13 + 5a + 3a2 = -5

Solving for variable 'a'.

Reorder the terms:
-13 + 5 + 5a + 3a2 = -5 + 5

Combine like terms: -13 + 5 = -8
-8 + 5a + 3a2 = -5 + 5

Combine like terms: -5 + 5 = 0
-8 + 5a + 3a2 = 0

Factor a trinomial.
(-8 + -3a)(1 + -1a) = 0

Subproblem 1
Set the factor '(-8 + -3a)' equal to zero and attempt to solve:

Simplifying
-8 + -3a = 0

Solving
-8 + -3a = 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 + -3a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3a = 0 + 8
-3a = 0 + 8

Combine like terms: 0 + 8 = 8
-3a = 8

Divide each side by '-3'.
a = -2.666666667

Simplifying
a = -2.666666667
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {-2.666666667, 1}