5y^2-10=13y-4

Solution for 5y^2-10=13y-4 equation:

Simplifying
5y2 + -10 = 13y + -4

Reorder the terms:
-10 + 5y2 = 13y + -4

Reorder the terms:
-10 + 5y2 = -4 + 13y

Solving
-10 + 5y2 = -4 + 13y

Solving for variable 'y'.

Reorder the terms:
-10 + 4 + -13y + 5y2 = -4 + 13y + 4 + -13y

Combine like terms: -10 + 4 = -6
-6 + -13y + 5y2 = -4 + 13y + 4 + -13y

Reorder the terms:
-6 + -13y + 5y2 = -4 + 4 + 13y + -13y

Combine like terms: -4 + 4 = 0
-6 + -13y + 5y2 = 0 + 13y + -13y
-6 + -13y + 5y2 = 13y + -13y

Combine like terms: 13y + -13y = 0
-6 + -13y + 5y2 = 0

Factor a trinomial.
(-2 + -5y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-2 + -5y)' equal to zero and attempt to solve:

Simplifying
-2 + -5y = 0

Solving
-2 + -5y = 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 + -5y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5y = 0 + 2
-5y = 0 + 2

Combine like terms: 0 + 2 = 2
-5y = 2

Divide each side by '-5'.
y = -0.4

Simplifying
y = -0.4
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-0.4, 3}