5(2y+3)(5y-2)=84

Simple and best practice solution for 5(2y+3)(5y-2)=84 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 5(2y+3)(5y-2)=84 equation:


Simplifying
5(2y + 3)(5y + -2) = 84

Reorder the terms:
5(3 + 2y)(5y + -2) = 84

Reorder the terms:
5(3 + 2y)(-2 + 5y) = 84

Multiply (3 + 2y) * (-2 + 5y)
5(3(-2 + 5y) + 2y * (-2 + 5y)) = 84
5((-2 * 3 + 5y * 3) + 2y * (-2 + 5y)) = 84
5((-6 + 15y) + 2y * (-2 + 5y)) = 84
5(-6 + 15y + (-2 * 2y + 5y * 2y)) = 84
5(-6 + 15y + (-4y + 10y2)) = 84

Combine like terms: 15y + -4y = 11y
5(-6 + 11y + 10y2) = 84
(-6 * 5 + 11y * 5 + 10y2 * 5) = 84
(-30 + 55y + 50y2) = 84

Solving
-30 + 55y + 50y2 = 84

Solving for variable 'y'.

Reorder the terms:
-30 + -84 + 55y + 50y2 = 84 + -84

Combine like terms: -30 + -84 = -114
-114 + 55y + 50y2 = 84 + -84

Combine like terms: 84 + -84 = 0
-114 + 55y + 50y2 = 0

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

Divide each side by '50'.
-2.28 + 1.1y + y2 = 0.0

Move the constant term to the right:

Add '2.28' to each side of the equation.
-2.28 + 1.1y + 2.28 + y2 = 0.0 + 2.28

Reorder the terms:
-2.28 + 2.28 + 1.1y + y2 = 0.0 + 2.28

Combine like terms: -2.28 + 2.28 = 0.00
0.00 + 1.1y + y2 = 0.0 + 2.28
1.1y + y2 = 0.0 + 2.28

Combine like terms: 0.0 + 2.28 = 2.28
1.1y + y2 = 2.28

The y term is 1.1y.  Take half its coefficient (0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
1.1y + 0.3025 + y2 = 2.28 + 0.3025

Reorder the terms:
0.3025 + 1.1y + y2 = 2.28 + 0.3025

Combine like terms: 2.28 + 0.3025 = 2.5825
0.3025 + 1.1y + y2 = 2.5825

Factor a perfect square on the left side:
(y + 0.55)(y + 0.55) = 2.5825

Calculate the square root of the right side: 1.607015868

Break this problem into two subproblems by setting 
(y + 0.55) equal to 1.607015868 and -1.607015868.

Subproblem 1

y + 0.55 = 1.607015868 Simplifying y + 0.55 = 1.607015868 Reorder the terms: 0.55 + y = 1.607015868 Solving 0.55 + y = 1.607015868 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + y = 1.607015868 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + y = 1.607015868 + -0.55 y = 1.607015868 + -0.55 Combine like terms: 1.607015868 + -0.55 = 1.057015868 y = 1.057015868 Simplifying y = 1.057015868

Subproblem 2

y + 0.55 = -1.607015868 Simplifying y + 0.55 = -1.607015868 Reorder the terms: 0.55 + y = -1.607015868 Solving 0.55 + y = -1.607015868 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.55' to each side of the equation. 0.55 + -0.55 + y = -1.607015868 + -0.55 Combine like terms: 0.55 + -0.55 = 0.00 0.00 + y = -1.607015868 + -0.55 y = -1.607015868 + -0.55 Combine like terms: -1.607015868 + -0.55 = -2.157015868 y = -2.157015868 Simplifying y = -2.157015868

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.057015868, -2.157015868}

See similar equations:

| 21+3y=12 | | 4x-1=10x+2 | | 4x(x^2-2)= | | 5(1+4p)-4p=-91 | | -4+3=23 | | 2x-5(x-3)=-5+2x+10 | | (4x+5y)(x+y)= | | F(x)=4x^2+14+12 | | 3x-6=9x-9 | | 2(5k+2)-15k+8+4= | | c+4=24 | | -4+p=23 | | 2x-4x+12+8x-5x-9= | | -100+4x=60 | | a+36=65 | | 6(j+3)-4j=24 | | 7z-7=2 | | -100+4x=25 | | 6(j+3)-4=24 | | 7b-0.40=6b-1.40 | | 7h+2f+3c+2g=17.20 | | 2y+8=6x | | (x+3)(x-12)= | | 9m=13n | | x^2=-3v | | 2-2s=0.75s+13 | | -9/4*1/6= | | 9(3+r)= | | 16x+41=3x+5y | | 3x-10y=-63 | | 18x+9-7x+6=81 | | 11(3-s)= |

Equations solver categories