4a^2+10a-84=0

Solution for 4a^2+10a-84=0 equation:

Simplifying
4a2 + 10a + -84 = 0

Reorder the terms:
-84 + 10a + 4a2 = 0

Solving
-84 + 10a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + 5a + 2a2) = 0

Factor a trinomial.
2((-6 + -1a)(7 + -2a)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(7 + -2a)' equal to zero and attempt to solve:

Simplifying
7 + -2a = 0

Solving
7 + -2a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2a = 0 + -7
-2a = 0 + -7

Combine like terms: 0 + -7 = -7
-2a = -7

Divide each side by '-2'.
a = 3.5

Simplifying
a = 3.5
Solution
a = {-6, 3.5}