4x(x+3)+4x(2x+1)=56

Simple and best practice solution for 4x(x+3)+4x(2x+1)=56 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 4x(x+3)+4x(2x+1)=56 equation: 


Simplifying
4x(x + 3) + 4x(2x + 1) = 56

Reorder the terms:
4x(3 + x) + 4x(2x + 1) = 56
(3 * 4x + x * 4x) + 4x(2x + 1) = 56
(12x + 4x2) + 4x(2x + 1) = 56

Reorder the terms:
12x + 4x2 + 4x(1 + 2x) = 56
12x + 4x2 + (1 * 4x + 2x * 4x) = 56
12x + 4x2 + (4x + 8x2) = 56

Reorder the terms:
12x + 4x + 4x2 + 8x2 = 56

Combine like terms: 12x + 4x = 16x
16x + 4x2 + 8x2 = 56

Combine like terms: 4x2 + 8x2 = 12x2
16x + 12x2 = 56

Solving
16x + 12x2 = 56

Solving for variable 'x'.

Reorder the terms:
-56 + 16x + 12x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + 16x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 4x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-14 + 4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-14 + 4x + 3x2 = 0

Solving
-14 + 4x + 3x2 = 0

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

Divide each side by '3'.
-4.666666667 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + 1.333333333x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + 1.333333333x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 4.666666667
1.333333333x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
1.333333333x + x2 = 4.666666667

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 4.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 4.666666667 + 0.4444444442

Combine like terms: 4.666666667 + 0.4444444442 = 5.1111111112
0.4444444442 + 1.333333333x + x2 = 5.1111111112

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 5.1111111112

Calculate the square root of the right side: 2.260776661

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 2.260776661 and -2.260776661.


Subproblem 1
x + 0.6666666665 = 2.260776661

Simplifying
x + 0.6666666665 = 2.260776661

Reorder the terms:
0.6666666665 + x = 2.260776661

Solving
0.6666666665 + x = 2.260776661

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 2.260776661 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 2.260776661 + -0.6666666665
x = 2.260776661 + -0.6666666665

Combine like terms: 2.260776661 + -0.6666666665 = 1.5941099945
x = 1.5941099945

Simplifying
x = 1.5941099945


Subproblem 2
x + 0.6666666665 = -2.260776661

Simplifying
x + 0.6666666665 = -2.260776661

Reorder the terms:
0.6666666665 + x = -2.260776661

Solving
0.6666666665 + x = -2.260776661

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -2.260776661 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -2.260776661 + -0.6666666665
x = -2.260776661 + -0.6666666665

Combine like terms: -2.260776661 + -0.6666666665 = -2.9274433275
x = -2.9274433275

Simplifying
x = -2.9274433275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5941099945, -2.9274433275}
Solution
x = {1.5941099945, -2.9274433275}

See similar equations:

| 31=-2x-5 | | [2x-5]=4 | | 2(x+2)=7(x-1)-19 | | S=3*L*w+3*w*h+5*h*Lforh | | -5y=-6x+5 | | 10a^2+19=8 | | (x-24)29=296 | | 9w-7=-2(w+9) | | 1.5x+400=1.5x+300 | | 4-3v(2+5v)+7= | | 5b-6=3 | | -2x-6y=-24 | | (x-24-29)=296 | | 8n^2+11n-2=-12 | | 1x+250=2x+300 | | -63=3(n-3) | | (x-24+29)=296 | | 3y-12=-x | | 1.5x+250=2.5x+300 | | 18=-9+9p | | 2m-3=10 | | 3k^2-13k-56=0 | | -14=-3+v | | 30=-10(x-6) | | 6(3+1)=3(4x+2) | | 3x+6=7-6 | | 16x-(6x-8)=68 | | 2n^2-40=11n | | 12+13=-32+10x | | 2(-10+x)=-24 | | X+Y-13=0 | | 4-2n=-1-n |

Equations solver categories