51-y(3y+4)=2(17-2y)-58

Solution for 51-y(3y+4)=2(17-2y)-58 equation:

Simplifying
51 + -1y(3y + 4) = 2(17 + -2y) + -58

Reorder the terms:
51 + -1y(4 + 3y) = 2(17 + -2y) + -58
51 + (4 * -1y + 3y * -1y) = 2(17 + -2y) + -58
51 + (-4y + -3y2) = 2(17 + -2y) + -58
51 + -4y + -3y2 = (17 * 2 + -2y * 2) + -58
51 + -4y + -3y2 = (34 + -4y) + -58

Reorder the terms:
51 + -4y + -3y2 = 34 + -58 + -4y

Combine like terms: 34 + -58 = -24
51 + -4y + -3y2 = -24 + -4y

Add '4y' to each side of the equation.
51 + -4y + 4y + -3y2 = -24 + -4y + 4y

Combine like terms: -4y + 4y = 0
51 + 0 + -3y2 = -24 + -4y + 4y
51 + -3y2 = -24 + -4y + 4y

Combine like terms: -4y + 4y = 0
51 + -3y2 = -24 + 0
51 + -3y2 = -24

Solving
51 + -3y2 = -24

Solving for variable 'y'.

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

Add '-51' to each side of the equation.
51 + -51 + -3y2 = -24 + -51

Combine like terms: 51 + -51 = 0
0 + -3y2 = -24 + -51
-3y2 = -24 + -51

Combine like terms: -24 + -51 = -75
-3y2 = -75

Divide each side by '-3'.
y2 = 25

Simplifying
y2 = 25

Take the square root of each side:
y = {-5, 5}