2y^2+7y+10=[y+4]

Solution for 2y^2+7y+10=[y+4] equation:

Simplifying
2y2 + 7y + 10 = [y + 4]

Reorder the terms:
10 + 7y + 2y2 = [y + 4]

Reorder the terms:
10 + 7y + 2y2 = [4 + y]

Remove brackets around [4 + y]
10 + 7y + 2y2 = 4 + y

Solving
10 + 7y + 2y2 = 4 + y

Solving for variable 'y'.

Reorder the terms:
10 + -4 + 7y + -1y + 2y2 = 4 + y + -4 + -1y

Combine like terms: 10 + -4 = 6
6 + 7y + -1y + 2y2 = 4 + y + -4 + -1y

Combine like terms: 7y + -1y = 6y
6 + 6y + 2y2 = 4 + y + -4 + -1y

Reorder the terms:
6 + 6y + 2y2 = 4 + -4 + y + -1y

Combine like terms: 4 + -4 = 0
6 + 6y + 2y2 = 0 + y + -1y
6 + 6y + 2y2 = y + -1y

Combine like terms: y + -1y = 0
6 + 6y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 3y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 3y + y2)' equal to zero and attempt to solve:

Simplifying
3 + 3y + y2 = 0

Solving
3 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 3y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + 3y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3y + y2 = 0 + -3
3y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
3y + y2 = -3

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = -3 + 2.25

Reorder the terms:
2.25 + 3y + y2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + 3y + y2 = -0.75

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.