16a^2+52a-43=5

Solution for 16a^2+52a-43=5 equation:

Simplifying
16a2 + 52a + -43 = 5

Reorder the terms:
-43 + 52a + 16a2 = 5

Solving
-43 + 52a + 16a2 = 5

Solving for variable 'a'.

Reorder the terms:
-43 + -5 + 52a + 16a2 = 5 + -5

Combine like terms: -43 + -5 = -48
-48 + 52a + 16a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-48 + 52a + 16a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 13a + 4a2) = 0

Factor a trinomial.
4((-4 + -1a)(3 + -4a)) = 0

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

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
Subproblem 2
Set the factor '(3 + -4a)' equal to zero and attempt to solve:

Simplifying
3 + -4a = 0

Solving
3 + -4a = 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 + -4a = 0 + -3

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

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

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
Solution
a = {-4, 0.75}