a^2+6a=4a-1

Solution for a^2+6a=4a-1 equation:

Simplifying
a2 + 6a = 4a + -1

Reorder the terms:
6a + a2 = 4a + -1

Reorder the terms:
6a + a2 = -1 + 4a

Solving
6a + a2 = -1 + 4a

Solving for variable 'a'.

Reorder the terms:
1 + 6a + -4a + a2 = -1 + 4a + 1 + -4a

Combine like terms: 6a + -4a = 2a
1 + 2a + a2 = -1 + 4a + 1 + -4a

Reorder the terms:
1 + 2a + a2 = -1 + 1 + 4a + -4a

Combine like terms: -1 + 1 = 0
1 + 2a + a2 = 0 + 4a + -4a
1 + 2a + a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
1 + 2a + a2 = 0

Factor a trinomial.
(1 + a)(1 + a) = 0

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

Simplifying
1 + a = 0

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

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

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

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

Simplifying
1 + a = 0

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

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

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

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