32y^2-5y+3=19y-1

Solution for 32y^2-5y+3=19y-1 equation:

Simplifying
32y2 + -5y + 3 = 19y + -1

Reorder the terms:
3 + -5y + 32y2 = 19y + -1

Reorder the terms:
3 + -5y + 32y2 = -1 + 19y

Solving
3 + -5y + 32y2 = -1 + 19y

Solving for variable 'y'.

Reorder the terms:
3 + 1 + -5y + -19y + 32y2 = -1 + 19y + 1 + -19y

Combine like terms: 3 + 1 = 4
4 + -5y + -19y + 32y2 = -1 + 19y + 1 + -19y

Combine like terms: -5y + -19y = -24y
4 + -24y + 32y2 = -1 + 19y + 1 + -19y

Reorder the terms:
4 + -24y + 32y2 = -1 + 1 + 19y + -19y

Combine like terms: -1 + 1 = 0
4 + -24y + 32y2 = 0 + 19y + -19y
4 + -24y + 32y2 = 19y + -19y

Combine like terms: 19y + -19y = 0
4 + -24y + 32y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + -6y + 8y2) = 0

Factor a trinomial.
4((1 + -4y)(1 + -2y)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -4y)' equal to zero and attempt to solve:

Simplifying
1 + -4y = 0

Solving
1 + -4y = 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 + -4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4y = 0 + -1
-4y = 0 + -1

Combine like terms: 0 + -1 = -1
-4y = -1

Divide each side by '-4'.
y = 0.25

Simplifying
y = 0.25
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 = {0.25, 0.5}