14x(x+3)=7

Simple and best practice solution for 14x(x+3)=7 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 14x(x+3)=7 equation: 


Simplifying
14x(x + 3) = 7

Reorder the terms:
14x(3 + x) = 7
(3 * 14x + x * 14x) = 7
(42x + 14x2) = 7

Solving
42x + 14x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 42x + 14x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 42x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-1 + 6x + 2x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-1 + 6x + 2x2)' equal to zero and attempt to solve:

Simplifying
-1 + 6x + 2x2 = 0

Solving
-1 + 6x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + 3x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 3x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3x + x2 = 0 + 0.5
3x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3x + x2 = 0.5

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 = 0.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + 3x + x2 = 2.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.658312395 and -1.658312395.


Subproblem 1
x + 1.5 = 1.658312395

Simplifying
x + 1.5 = 1.658312395

Reorder the terms:
1.5 + x = 1.658312395

Solving
1.5 + x = 1.658312395

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 = 1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.658312395 + -1.5
x = 1.658312395 + -1.5

Combine like terms: 1.658312395 + -1.5 = 0.158312395
x = 0.158312395

Simplifying
x = 0.158312395


Subproblem 2
x + 1.5 = -1.658312395

Simplifying
x + 1.5 = -1.658312395

Reorder the terms:
1.5 + x = -1.658312395

Solving
1.5 + x = -1.658312395

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 = -1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.658312395 + -1.5
x = -1.658312395 + -1.5

Combine like terms: -1.658312395 + -1.5 = -3.158312395
x = -3.158312395

Simplifying
x = -3.158312395


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.158312395, -3.158312395}
Solution
x = {0.158312395, -3.158312395}

See similar equations:

| -3g^2+13g-10=0 | | 0.17x-0.58=1.42x-0.74x-3.522 | | -8(2v-7)=22-3v | | -10y+7=9-3y | | 3xy-3= | | 2.21-1.14x=4x-4.215 | | 6y-3=5y+8 | | 8r+2-4=27 | | 5.12x+7.56=2.6x | | 1.6x+9.4=3.5x-2 | | -11x=x | | 7(d-5)+11=5 | | c^2+c+4=0 | | -31-8s=3(5s+7) | | -10f=-40 | | 6x+25+1=3x+12-3 | | 2h+4=8 | | -2(6f-7)=22 | | 4(6x+3)-14(x+2)=2(10-x) | | 4(3x-15)+2=2x+7 | | 6-2x=15-5(3+2x) | | 4d+13.00-6.00=13.20 | | 5-6z7=17-6z5 | | 12x-3=7x+12 | | 4x+3=5+3(x+7) | | -5+-1= | | -4(3-5a)=17 | | -42/-21= | | 2k=8 | | 4a-1=-73 | | 3x-57+x+15=2 | | n^2-3n+70=0 |

Equations solver categories