4a^2-36a=-56

Solution for 4a^2-36a=-56 equation:

Simplifying
4a2 + -36a = -56

Reorder the terms:
-36a + 4a2 = -56

Solving
-36a + 4a2 = -56

Solving for variable 'a'.

Reorder the terms:
56 + -36a + 4a2 = -56 + 56

Combine like terms: -56 + 56 = 0
56 + -36a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(14 + -9a + a2) = 0

Factor a trinomial.
4((2 + -1a)(7 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

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

Simplifying
7 + -1a = 0

Solving
7 + -1a = 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 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {2, 7}