(2y-1)(y+4)=y^2+7y

Solution for (2y-1)(y+4)=y^2+7y equation:

Simplifying
(2y + -1)(y + 4) = y2 + 7y

Reorder the terms:
(-1 + 2y)(y + 4) = y2 + 7y

Reorder the terms:
(-1 + 2y)(4 + y) = y2 + 7y

Multiply (-1 + 2y) * (4 + y)
(-1(4 + y) + 2y * (4 + y)) = y2 + 7y
((4 * -1 + y * -1) + 2y * (4 + y)) = y2 + 7y
((-4 + -1y) + 2y * (4 + y)) = y2 + 7y
(-4 + -1y + (4 * 2y + y * 2y)) = y2 + 7y
(-4 + -1y + (8y + 2y2)) = y2 + 7y

Combine like terms: -1y + 8y = 7y
(-4 + 7y + 2y2) = y2 + 7y

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

Add '-7y' to each side of the equation.
-4 + 7y + -7y + 2y2 = 7y + -7y + y2

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

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

Solving
-4 + 2y2 = y2

Solving for variable 'y'.

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

Add '-1y2' to each side of the equation.
-4 + 2y2 + -1y2 = y2 + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-4 + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-4 + 1y2 = 0

Add '4' to each side of the equation.
-4 + 4 + 1y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1y2 = 0 + 4
1y2 = 0 + 4

Combine like terms: 0 + 4 = 4
1y2 = 4

Divide each side by '1'.
y2 = 4

Simplifying
y2 = 4

Take the square root of each side:
y = {-2, 2}