3(4y^2+9)-5y(2y+3)=24+16y

Simple and best practice solution for 3(4y^2+9)-5y(2y+3)=24+16y equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 3(4y^2+9)-5y(2y+3)=24+16y equation:


Simplifying
3(4y2 + 9) + -5y(2y + 3) = 24 + 16y

Reorder the terms:
3(9 + 4y2) + -5y(2y + 3) = 24 + 16y
(9 * 3 + 4y2 * 3) + -5y(2y + 3) = 24 + 16y
(27 + 12y2) + -5y(2y + 3) = 24 + 16y

Reorder the terms:
27 + 12y2 + -5y(3 + 2y) = 24 + 16y
27 + 12y2 + (3 * -5y + 2y * -5y) = 24 + 16y
27 + 12y2 + (-15y + -10y2) = 24 + 16y

Reorder the terms:
27 + -15y + 12y2 + -10y2 = 24 + 16y

Combine like terms: 12y2 + -10y2 = 2y2
27 + -15y + 2y2 = 24 + 16y

Solving
27 + -15y + 2y2 = 24 + 16y

Solving for variable 'y'.

Reorder the terms:
27 + -24 + -15y + -16y + 2y2 = 24 + 16y + -24 + -16y

Combine like terms: 27 + -24 = 3
3 + -15y + -16y + 2y2 = 24 + 16y + -24 + -16y

Combine like terms: -15y + -16y = -31y
3 + -31y + 2y2 = 24 + 16y + -24 + -16y

Reorder the terms:
3 + -31y + 2y2 = 24 + -24 + 16y + -16y

Combine like terms: 24 + -24 = 0
3 + -31y + 2y2 = 0 + 16y + -16y
3 + -31y + 2y2 = 16y + -16y

Combine like terms: 16y + -16y = 0
3 + -31y + 2y2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
1.5 + -15.5y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -15.5y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -15.5y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -15.5y + y2 = 0 + -1.5
-15.5y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-15.5y + y2 = -1.5

The y term is -15.5y.  Take half its coefficient (-7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
-15.5y + 60.0625 + y2 = -1.5 + 60.0625

Reorder the terms:
60.0625 + -15.5y + y2 = -1.5 + 60.0625

Combine like terms: -1.5 + 60.0625 = 58.5625
60.0625 + -15.5y + y2 = 58.5625

Factor a perfect square on the left side:
(y + -7.75)(y + -7.75) = 58.5625

Calculate the square root of the right side: 7.652613933

Break this problem into two subproblems by setting 
(y + -7.75) equal to 7.652613933 and -7.652613933.

Subproblem 1

y + -7.75 = 7.652613933 Simplifying y + -7.75 = 7.652613933 Reorder the terms: -7.75 + y = 7.652613933 Solving -7.75 + y = 7.652613933 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + y = 7.652613933 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + y = 7.652613933 + 7.75 y = 7.652613933 + 7.75 Combine like terms: 7.652613933 + 7.75 = 15.402613933 y = 15.402613933 Simplifying y = 15.402613933

Subproblem 2

y + -7.75 = -7.652613933 Simplifying y + -7.75 = -7.652613933 Reorder the terms: -7.75 + y = -7.652613933 Solving -7.75 + y = -7.652613933 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + y = -7.652613933 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + y = -7.652613933 + 7.75 y = -7.652613933 + 7.75 Combine like terms: -7.652613933 + 7.75 = 0.097386067 y = 0.097386067 Simplifying y = 0.097386067

Solution

The solution to the problem is based on the solutions from the subproblems. y = {15.402613933, 0.097386067}

See similar equations:

| 8x+8y=56 | | =-16t^2+96t+3 | | z^-3/4 | | 3(x-5)+5=14(4x-5)+7(x-5) | | 7x=3(x+5) | | x-2+5x=628 | | 2sec=4 | | 3x+6y+2z=35 | | 4-2z=1 | | (8t-7)(3t-5)=0 | | 3*1/2-2X=1*1/4 | | 5ln(9x-2)+1=7 | | 8.1X^3-50x-33=0 | | (x^2-x+1)(-5-2x)+(1-5x-x^2)(2x-1)= | | 0.33x^2+0.71x-0.14=0 | | (1-5x-x^2)(2x-1)= | | 10=3(4x-6) | | 24.4=3x+0.4 | | (x^2-x+1)(-5-2x)= | | 6n+15=3n+21 | | 6(n+1)=3(n+9) | | 5x-y-7=0 | | 5(n+3)=2(2n+11) | | 4(n+2)=2(3n+2) | | 2x^2-8+8=0 | | 3(n+7)=6(n+2) | | 3(2n+5)=3(3n+7) | | 7(n+4)=2(3n+17) | | .75(x-2)-.8=x | | x^4=234 | | X^2(x-3)+20=0 | | -16t^2+104t+560= |

Equations solver categories