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

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

Simplifying
4y2 + -5y + 3 + 2y2 + 7y + -7 = 0

Reorder the terms:
3 + -7 + -5y + 7y + 4y2 + 2y2 = 0

Combine like terms: 3 + -7 = -4
-4 + -5y + 7y + 4y2 + 2y2 = 0

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

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

Solving
-4 + 2y + 6y2 = 0

Solving for variable 'y'.

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

Factor a trinomial.
2((-1 + -1y)(2 + -3y)) = 0

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 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 + -1y = 0 + 1

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

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

Divide each side by '-1'.
y = -1

Simplifying
y = -1
Subproblem 2
Set the factor '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3y = 0 + -2
-3y = 0 + -2

Combine like terms: 0 + -2 = -2
-3y = -2

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {-1, 0.6666666667}