4y^2-7y=15

Solution for 4y^2-7y=15 equation:

Simplifying
4y2 + -7y = 15

Reorder the terms:
-7y + 4y2 = 15

Solving
-7y + 4y2 = 15

Solving for variable 'y'.

Reorder the terms:
-15 + -7y + 4y2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -7y + 4y2 = 0

Factor a trinomial.
(-5 + -4y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-5 + -4y)' equal to zero and attempt to solve:

Simplifying
-5 + -4y = 0

Solving
-5 + -4y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4y = 0 + 5
-4y = 0 + 5

Combine like terms: 0 + 5 = 5
-4y = 5

Divide each side by '-4'.
y = -1.25

Simplifying
y = -1.25
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 = {-1.25, 3}