y+6=4y^2-7y+1

Solution for y+6=4y^2-7y+1 equation:

Simplifying
y + 6 = 4y2 + -7y + 1

Reorder the terms:
6 + y = 4y2 + -7y + 1

Reorder the terms:
6 + y = 1 + -7y + 4y2

Solving
6 + y = 1 + -7y + 4y2

Solving for variable 'y'.

Reorder the terms:
6 + -1 + y + 7y + -4y2 = 1 + -7y + 4y2 + -1 + 7y + -4y2

Combine like terms: 6 + -1 = 5
5 + y + 7y + -4y2 = 1 + -7y + 4y2 + -1 + 7y + -4y2

Combine like terms: y + 7y = 8y
5 + 8y + -4y2 = 1 + -7y + 4y2 + -1 + 7y + -4y2

Reorder the terms:
5 + 8y + -4y2 = 1 + -1 + -7y + 7y + 4y2 + -4y2

Combine like terms: 1 + -1 = 0
5 + 8y + -4y2 = 0 + -7y + 7y + 4y2 + -4y2
5 + 8y + -4y2 = -7y + 7y + 4y2 + -4y2

Combine like terms: -7y + 7y = 0
5 + 8y + -4y2 = 0 + 4y2 + -4y2
5 + 8y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
5 + 8y + -4y2 = 0

Factor a trinomial.
(5 + -2y)(1 + 2y) = 0

Subproblem 1
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 0

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

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

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

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

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {2.5, -0.5}