2y^2+7y+3(3y-4)=

Solution for 2y^2+7y+3(3y-4)= equation:

Simplifying
2y2 + 7y + 3(3y + -4) = 0

Reorder the terms:
2y2 + 7y + 3(-4 + 3y) = 0
2y2 + 7y + (-4 * 3 + 3y * 3) = 0
2y2 + 7y + (-12 + 9y) = 0

Reorder the terms:
-12 + 7y + 9y + 2y2 = 0

Combine like terms: 7y + 9y = 16y
-12 + 16y + 2y2 = 0

Solving
-12 + 16y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 8y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 8y + y2)' equal to zero and attempt to solve:

Simplifying
-6 + 8y + y2 = 0

Solving
-6 + 8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 8y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + 8y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 8y + y2 = 0 + 6
8y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
8y + y2 = 6

The y term is 8y.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8y + 16 + y2 = 6 + 16

Reorder the terms:
16 + 8y + y2 = 6 + 16

Combine like terms: 6 + 16 = 22
16 + 8y + y2 = 22

Factor a perfect square on the left side:
(y + 4)(y + 4) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(y + 4) equal to 4.69041576 and -4.69041576.

Subproblem 1
y + 4 = 4.69041576

Simplifying
y + 4 = 4.69041576

Reorder the terms:
4 + y = 4.69041576

Solving
4 + y = 4.69041576

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = 4.69041576 + -4

Combine like terms: 4 + -4 = 0
0 + y = 4.69041576 + -4
y = 4.69041576 + -4

Combine like terms: 4.69041576 + -4 = 0.69041576
y = 0.69041576

Simplifying
y = 0.69041576

Subproblem 2
y + 4 = -4.69041576

Simplifying
y + 4 = -4.69041576

Reorder the terms:
4 + y = -4.69041576

Solving
4 + y = -4.69041576

Solving for variable 'y'.

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

Add '-4' to each side of the equation.
4 + -4 + y = -4.69041576 + -4

Combine like terms: 4 + -4 = 0
0 + y = -4.69041576 + -4
y = -4.69041576 + -4

Combine like terms: -4.69041576 + -4 = -8.69041576
y = -8.69041576

Simplifying
y = -8.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.69041576, -8.69041576}
Solution
y = {0.69041576, -8.69041576}