7a^2-41a+27=-6a-1

Solution for 7a^2-41a+27=-6a-1 equation:

Simplifying
7a2 + -41a + 27 = -6a + -1

Reorder the terms:
27 + -41a + 7a2 = -6a + -1

Reorder the terms:
27 + -41a + 7a2 = -1 + -6a

Solving
27 + -41a + 7a2 = -1 + -6a

Solving for variable 'a'.

Reorder the terms:
27 + 1 + -41a + 6a + 7a2 = -1 + -6a + 1 + 6a

Combine like terms: 27 + 1 = 28
28 + -41a + 6a + 7a2 = -1 + -6a + 1 + 6a

Combine like terms: -41a + 6a = -35a
28 + -35a + 7a2 = -1 + -6a + 1 + 6a

Reorder the terms:
28 + -35a + 7a2 = -1 + 1 + -6a + 6a

Combine like terms: -1 + 1 = 0
28 + -35a + 7a2 = 0 + -6a + 6a
28 + -35a + 7a2 = -6a + 6a

Combine like terms: -6a + 6a = 0
28 + -35a + 7a2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(4 + -5a + a2) = 0

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

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
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
Solution
a = {1, 4}