4x^2+6x+6=x+5

Solution for 4x^2+6x+6=x+5 equation:

Simplifying
4x2 + 6x + 6 = x + 5

Reorder the terms:
6 + 6x + 4x2 = x + 5

Reorder the terms:
6 + 6x + 4x2 = 5 + x

Solving
6 + 6x + 4x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
6 + -5 + 6x + -1x + 4x2 = 5 + x + -5 + -1x

Combine like terms: 6 + -5 = 1
1 + 6x + -1x + 4x2 = 5 + x + -5 + -1x

Combine like terms: 6x + -1x = 5x
1 + 5x + 4x2 = 5 + x + -5 + -1x

Reorder the terms:
1 + 5x + 4x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
1 + 5x + 4x2 = 0 + x + -1x
1 + 5x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
1 + 5x + 4x2 = 0

Factor a trinomial.
(1 + x)(1 + 4x) = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-1, -0.25}