2d(24+3d)=84

Simple and best practice solution for 2d(24+3d)=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 2d(24+3d)=84 equation:


Simplifying
2d(24 + 3d) = 84
(24 * 2d + 3d * 2d) = 84
(48d + 6d2) = 84

Solving
48d + 6d2 = 84

Solving for variable 'd'.

Reorder the terms:
-84 + 48d + 6d2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 48d + 6d2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-14 + 8d + d2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-14 + 8d + d2)' equal to zero and attempt to solve: Simplifying -14 + 8d + d2 = 0 Solving -14 + 8d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 8d + 14 + d2 = 0 + 14 Reorder the terms: -14 + 14 + 8d + d2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 8d + d2 = 0 + 14 8d + d2 = 0 + 14 Combine like terms: 0 + 14 = 14 8d + d2 = 14 The d term is 8d. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8d + 16 + d2 = 14 + 16 Reorder the terms: 16 + 8d + d2 = 14 + 16 Combine like terms: 14 + 16 = 30 16 + 8d + d2 = 30 Factor a perfect square on the left side: (d + 4)(d + 4) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (d + 4) equal to 5.477225575 and -5.477225575.

Subproblem 1

d + 4 = 5.477225575 Simplifying d + 4 = 5.477225575 Reorder the terms: 4 + d = 5.477225575 Solving 4 + d = 5.477225575 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + d = 5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + d = 5.477225575 + -4 d = 5.477225575 + -4 Combine like terms: 5.477225575 + -4 = 1.477225575 d = 1.477225575 Simplifying d = 1.477225575

Subproblem 2

d + 4 = -5.477225575 Simplifying d + 4 = -5.477225575 Reorder the terms: 4 + d = -5.477225575 Solving 4 + d = -5.477225575 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + d = -5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + d = -5.477225575 + -4 d = -5.477225575 + -4 Combine like terms: -5.477225575 + -4 = -9.477225575 d = -9.477225575 Simplifying d = -9.477225575

Solution

The solution to the problem is based on the solutions from the subproblems. d = {1.477225575, -9.477225575}

Solution

d = {1.477225575, -9.477225575}

See similar equations:

| -4(-4x-1)=6x-26 | | 8=2c+4 | | 0.6x+16.2=x-4.08 | | 6x+6.2=2(4x-2.9) | | 2. 4(x+3)=3x+17 | | 3(x+3.21)=2x | | 2w^2-w-30=0 | | 2(x^2-6x+10)=0 | | 5x-5-7x=-8+3x-10 | | 3(x+2.24)=2x | | 0.2x+0.8=-1 | | -2(5s-5)-10=-18s-18-2 | | 3125=50*25*h | | 8(x-8.8)=3.2 | | t^3-12t^2+36t=24 | | t^3-12t^2+36+24=0 | | t^3-12t^2+36t-24=0 | | 6x+6.28=2x+12 | | -3x+4=-y | | -2.8x+2.1=-11.9 | | 3t^2+20t=0 | | 15z^2-37z+20=0 | | 5t^2+20t=0 | | -2.8+2.1=-11.9 | | 6+9k=8k+13 | | y^2-8y+80=0 | | 12x+13y=36.033 | | 12x+13y=26.033 | | 2m=4m-120 | | 13x+8y-5x+2y= | | 4m-120=5n | | 2x-x^2=.8 |

Equations solver categories