4y^3+5y^2-6y^3-7y+19y^3=

Solution for 4y^3+5y^2-6y^3-7y+19y^3= equation:

Simplifying
4y3 + 5y2 + -6y3 + -7y + 19y3 = 0

Reorder the terms:
-7y + 5y2 + 4y3 + -6y3 + 19y3 = 0

Combine like terms: 4y3 + -6y3 = -2y3
-7y + 5y2 + -2y3 + 19y3 = 0

Combine like terms: -2y3 + 19y3 = 17y3
-7y + 5y2 + 17y3 = 0

Solving
-7y + 5y2 + 17y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-7 + 5y + 17y2) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-7 + 5y + 17y2)' equal to zero and attempt to solve:

Simplifying
-7 + 5y + 17y2 = 0

Solving
-7 + 5y + 17y2 = 0

Begin completing the square.  Divide all terms by
17 the coefficient of the squared term: 

Divide each side by '17'.
-0.4117647059 + 0.2941176471y + y2 = 0

Move the constant term to the right:

Add '0.4117647059' to each side of the equation.
-0.4117647059 + 0.2941176471y + 0.4117647059 + y2 = 0 + 0.4117647059

Reorder the terms:
-0.4117647059 + 0.4117647059 + 0.2941176471y + y2 = 0 + 0.4117647059

Combine like terms: -0.4117647059 + 0.4117647059 = 0.0000000000
0.0000000000 + 0.2941176471y + y2 = 0 + 0.4117647059
0.2941176471y + y2 = 0 + 0.4117647059

Combine like terms: 0 + 0.4117647059 = 0.4117647059
0.2941176471y + y2 = 0.4117647059

The y term is 0.2941176471y.  Take half its coefficient (0.1470588236).
Square it (0.02162629760) and add it to both sides.

Add '0.02162629760' to each side of the equation.
0.2941176471y + 0.02162629760 + y2 = 0.4117647059 + 0.02162629760

Reorder the terms:
0.02162629760 + 0.2941176471y + y2 = 0.4117647059 + 0.02162629760

Combine like terms: 0.4117647059 + 0.02162629760 = 0.4333910035
0.02162629760 + 0.2941176471y + y2 = 0.4333910035

Factor a perfect square on the left side:
(y + 0.1470588236)(y + 0.1470588236) = 0.4333910035

Calculate the square root of the right side: 0.658324391

Break this problem into two subproblems by setting 
(y + 0.1470588236) equal to 0.658324391 and -0.658324391.

Subproblem 1
y + 0.1470588236 = 0.658324391

Simplifying
y + 0.1470588236 = 0.658324391

Reorder the terms:
0.1470588236 + y = 0.658324391

Solving
0.1470588236 + y = 0.658324391

Solving for variable 'y'.

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

Add '-0.1470588236' to each side of the equation.
0.1470588236 + -0.1470588236 + y = 0.658324391 + -0.1470588236

Combine like terms: 0.1470588236 + -0.1470588236 = 0.0000000000
0.0000000000 + y = 0.658324391 + -0.1470588236
y = 0.658324391 + -0.1470588236

Combine like terms: 0.658324391 + -0.1470588236 = 0.5112655674
y = 0.5112655674

Simplifying
y = 0.5112655674

Subproblem 2
y + 0.1470588236 = -0.658324391

Simplifying
y + 0.1470588236 = -0.658324391

Reorder the terms:
0.1470588236 + y = -0.658324391

Solving
0.1470588236 + y = -0.658324391

Solving for variable 'y'.

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

Add '-0.1470588236' to each side of the equation.
0.1470588236 + -0.1470588236 + y = -0.658324391 + -0.1470588236

Combine like terms: 0.1470588236 + -0.1470588236 = 0.0000000000
0.0000000000 + y = -0.658324391 + -0.1470588236
y = -0.658324391 + -0.1470588236

Combine like terms: -0.658324391 + -0.1470588236 = -0.8053832146
y = -0.8053832146

Simplifying
y = -0.8053832146

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.5112655674, -0.8053832146}
Solution
y = {0, 0.5112655674, -0.8053832146}