7x(16+3x)=21

Simple and best practice solution for 7x(16+3x)=21 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 7x(16+3x)=21 equation: 


Simplifying
7x(16 + 3x) = 21
(16 * 7x + 3x * 7x) = 21
(112x + 21x2) = 21

Solving
112x + 21x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + 112x + 21x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 112x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + 16x + 3x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-3 + 16x + 3x2)' equal to zero and attempt to solve:

Simplifying
-3 + 16x + 3x2 = 0

Solving
-3 + 16x + 3x2 = 0

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

Divide each side by '3'.
-1 + 5.333333333x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 5.333333333x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 5.333333333x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5.333333333x + x2 = 0 + 1
5.333333333x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
5.333333333x + x2 = 1

The x term is 5.333333333x.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333x + 7.111111113 + x2 = 1 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333x + x2 = 1 + 7.111111113

Combine like terms: 1 + 7.111111113 = 8.111111113
7.111111113 + 5.333333333x + x2 = 8.111111113

Factor a perfect square on the left side:
(x + 2.666666667)(x + 2.666666667) = 8.111111113

Calculate the square root of the right side: 2.848001249

Break this problem into two subproblems by setting 
(x + 2.666666667) equal to 2.848001249 and -2.848001249.


Subproblem 1
x + 2.666666667 = 2.848001249

Simplifying
x + 2.666666667 = 2.848001249

Reorder the terms:
2.666666667 + x = 2.848001249

Solving
2.666666667 + x = 2.848001249

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = 2.848001249 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = 2.848001249 + -2.666666667
x = 2.848001249 + -2.666666667

Combine like terms: 2.848001249 + -2.666666667 = 0.181334582
x = 0.181334582

Simplifying
x = 0.181334582


Subproblem 2
x + 2.666666667 = -2.848001249

Simplifying
x + 2.666666667 = -2.848001249

Reorder the terms:
2.666666667 + x = -2.848001249

Solving
2.666666667 + x = -2.848001249

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = -2.848001249 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = -2.848001249 + -2.666666667
x = -2.848001249 + -2.666666667

Combine like terms: -2.848001249 + -2.666666667 = -5.514667916
x = -5.514667916

Simplifying
x = -5.514667916


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.181334582, -5.514667916}
Solution
x = {0.181334582, -5.514667916}

See similar equations:

| 3m(12-3)=4m-4 | | 3x+5=-16 | | 8-(4y-1)=4-5y | | (4x+5)(x-2)=4x(x-2) | | 2+x=12 | | 4x+3=11+2x | | 6x+2=5x | | 8=x+15 | | 6+2(3x-8)=2x+18 | | 5x+4=34 | | x+.125=-.75 | | 7a-14=56 | | -4(x-8)-(6+6x)=-11x | | (5x+9)*-3=-1(2) | | -4.1x=-4x+4.5 | | -4.1x=-4x+4.5 | | 4.6x+3=3.6x | | 4y*5+2y*3= | | 6x-8=17+x | | 5x(6+2x)=60 | | 4+3y=19 | | x-13=-37 | | 2x+26=-11x | | 5x(6+2)=60 | | 4s+51+6s=17+8s | | 2+5(x-13)=x-3 | | 0.03(x-15)=.6 | | -5+2(x+4)=3+2x | | 6x+2=50 | | 3n+4n=27 | | -7y+5=-8y+8 | | 5+2(x-4)=4+2x |

Equations solver categories