8(y^2)-12y+4=y+10

Solution for 8(y^2)-12y+4=y+10 equation:

Simplifying
8(y2) + -12y + 4 = y + 10

Reorder the terms:
4 + -12y + 8y2 = y + 10

Reorder the terms:
4 + -12y + 8y2 = 10 + y

Solving
4 + -12y + 8y2 = 10 + y

Solving for variable 'y'.

Reorder the terms:
4 + -10 + -12y + -1y + 8y2 = 10 + y + -10 + -1y

Combine like terms: 4 + -10 = -6
-6 + -12y + -1y + 8y2 = 10 + y + -10 + -1y

Combine like terms: -12y + -1y = -13y
-6 + -13y + 8y2 = 10 + y + -10 + -1y

Reorder the terms:
-6 + -13y + 8y2 = 10 + -10 + y + -1y

Combine like terms: 10 + -10 = 0
-6 + -13y + 8y2 = 0 + y + -1y
-6 + -13y + 8y2 = y + -1y

Combine like terms: y + -1y = 0
-6 + -13y + 8y2 = 0

Factor a trinomial.
(-3 + -8y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-3 + -8y)' equal to zero and attempt to solve:

Simplifying
-3 + -8y = 0

Solving
-3 + -8y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -8y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8y = 0 + 3
-8y = 0 + 3

Combine like terms: 0 + 3 = 3
-8y = 3

Divide each side by '-8'.
y = -0.375

Simplifying
y = -0.375
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-0.375, 2}