36a+42a^2-78=

Solution for 36a+42a^2-78= equation:

Simplifying
36a + 42a2 + -78 = 0

Reorder the terms:
-78 + 36a + 42a2 = 0

Solving
-78 + 36a + 42a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-13 + 6a + 7a2) = 0

Factor a trinomial.
6((-13 + -7a)(1 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-13 + -7a)' equal to zero and attempt to solve:

Simplifying
-13 + -7a = 0

Solving
-13 + -7a = 0

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

Add '13' to each side of the equation.
-13 + 13 + -7a = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -7a = 0 + 13
-7a = 0 + 13

Combine like terms: 0 + 13 = 13
-7a = 13

Divide each side by '-7'.
a = -1.857142857

Simplifying
a = -1.857142857
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 = {-1.857142857, 1}