(4y^2-9)-(y^2+25)+23=0

Solution for (4y^2-9)-(y^2+25)+23=0 equation:

Simplifying
(4y2 + -9) + -1(y2 + 25) + 23 = 0

Reorder the terms:
(-9 + 4y2) + -1(y2 + 25) + 23 = 0

Remove parenthesis around (-9 + 4y2)
-9 + 4y2 + -1(y2 + 25) + 23 = 0

Reorder the terms:
-9 + 4y2 + -1(25 + y2) + 23 = 0
-9 + 4y2 + (25 * -1 + y2 * -1) + 23 = 0
-9 + 4y2 + (-25 + -1y2) + 23 = 0

Reorder the terms:
-9 + -25 + 23 + 4y2 + -1y2 = 0

Combine like terms: -9 + -25 = -34
-34 + 23 + 4y2 + -1y2 = 0

Combine like terms: -34 + 23 = -11
-11 + 4y2 + -1y2 = 0

Combine like terms: 4y2 + -1y2 = 3y2
-11 + 3y2 = 0

Solving
-11 + 3y2 = 0

Solving for variable 'y'.

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

Add '11' to each side of the equation.
-11 + 11 + 3y2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 3y2 = 0 + 11
3y2 = 0 + 11

Combine like terms: 0 + 11 = 11
3y2 = 11

Divide each side by '3'.
y2 = 3.666666667

Simplifying
y2 = 3.666666667

Take the square root of each side:
y = {-1.914854216, 1.914854216}