21(x+3)x=180

Simple and best practice solution for 21(x+3)x=180 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 21(x+3)x=180 equation: 


Simplifying
21(x + 3) * x = 180

Reorder the terms:
21(3 + x) * x = 180

Reorder the terms for easier multiplication:
21x(3 + x) = 180
(3 * 21x + x * 21x) = 180
(63x + 21x2) = 180

Solving
63x + 21x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 63x + 21x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 63x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 21x + 7x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + 21x + 7x2)' equal to zero and attempt to solve:

Simplifying
-60 + 21x + 7x2 = 0

Solving
-60 + 21x + 7x2 = 0

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

Divide each side by '7'.
-8.571428571 + 3x + x2 = 0

Move the constant term to the right:

Add '8.571428571' to each side of the equation.
-8.571428571 + 3x + 8.571428571 + x2 = 0 + 8.571428571

Reorder the terms:
-8.571428571 + 8.571428571 + 3x + x2 = 0 + 8.571428571

Combine like terms: -8.571428571 + 8.571428571 = 0.000000000
0.000000000 + 3x + x2 = 0 + 8.571428571
3x + x2 = 0 + 8.571428571

Combine like terms: 0 + 8.571428571 = 8.571428571
3x + x2 = 8.571428571

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 8.571428571 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 8.571428571 + 2.25

Combine like terms: 8.571428571 + 2.25 = 10.821428571
2.25 + 3x + x2 = 10.821428571

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 10.821428571

Calculate the square root of the right side: 3.289593983

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.289593983 and -3.289593983.


Subproblem 1
x + 1.5 = 3.289593983

Simplifying
x + 1.5 = 3.289593983

Reorder the terms:
1.5 + x = 3.289593983

Solving
1.5 + x = 3.289593983

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 3.289593983 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.289593983 + -1.5
x = 3.289593983 + -1.5

Combine like terms: 3.289593983 + -1.5 = 1.789593983
x = 1.789593983

Simplifying
x = 1.789593983


Subproblem 2
x + 1.5 = -3.289593983

Simplifying
x + 1.5 = -3.289593983

Reorder the terms:
1.5 + x = -3.289593983

Solving
1.5 + x = -3.289593983

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -3.289593983 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.289593983 + -1.5
x = -3.289593983 + -1.5

Combine like terms: -3.289593983 + -1.5 = -4.789593983
x = -4.789593983

Simplifying
x = -4.789593983


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.789593983, -4.789593983}
Solution
x = {1.789593983, -4.789593983}

See similar equations:

| (y-4)/3+2=(y-5)/6 | | 363m^2-27= | | 3msquared-16m+21=0 | | 21(x+3)+x=180 | | y-4/3+2=y-5/6 | | 384w^2-150= | | 41-1q=3q-15 | | x=-y-1 | | .4s=-10 | | -5(x+2)-12=15+3 | | 3x+4+5+6= | | 3/5-15=6/5x+12 | | 2a+6=5a-8 | | -n+4n=(-1+4)n | | -9=15+3*2i | | 5p/6+26=-4 | | 6v^2-150= | | 4y-3+27=6y+8-y | | 2x-66987=29811 | | 8x^2-80x+195=-5 | | 8y-7y=(8-7) | | -6x-1=-36+x | | -9=3+6x | | 16m-9=-2m | | 5t-7t=(5-7) | | 16m-9=-2 | | 16+15x= | | 27v^2-75w^2= | | 8y-7y=(8-7)y | | 1/c+3=7/42 | | -6=b+1-6 | | 5+3c= |

Equations solver categories