15x^2+102x-72=0

Simple and best practice solution for 15x^2+102x-72=0 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 15x^2+102x-72=0 equation: 


Simplifying
15x2 + 102x + -72 = 0

Reorder the terms:
-72 + 102x + 15x2 = 0

Solving
-72 + 102x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 34x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-24 + 34x + 5x2)' equal to zero and attempt to solve:

Simplifying
-24 + 34x + 5x2 = 0

Solving
-24 + 34x + 5x2 = 0

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

Divide each side by '5'.
-4.8 + 6.8x + x2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + 6.8x + 4.8 + x2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + 6.8x + x2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + 6.8x + x2 = 0 + 4.8
6.8x + x2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
6.8x + x2 = 4.8

The x term is 6.8x.  Take half its coefficient (3.4).
Square it (11.56) and add it to both sides.

Add '11.56' to each side of the equation.
6.8x + 11.56 + x2 = 4.8 + 11.56

Reorder the terms:
11.56 + 6.8x + x2 = 4.8 + 11.56

Combine like terms: 4.8 + 11.56 = 16.36
11.56 + 6.8x + x2 = 16.36

Factor a perfect square on the left side:
(x + 3.4)(x + 3.4) = 16.36

Calculate the square root of the right side: 4.044749683

Break this problem into two subproblems by setting 
(x + 3.4) equal to 4.044749683 and -4.044749683.


Subproblem 1
x + 3.4 = 4.044749683

Simplifying
x + 3.4 = 4.044749683

Reorder the terms:
3.4 + x = 4.044749683

Solving
3.4 + x = 4.044749683

Solving for variable 'x'.

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

Add '-3.4' to each side of the equation.
3.4 + -3.4 + x = 4.044749683 + -3.4

Combine like terms: 3.4 + -3.4 = 0.0
0.0 + x = 4.044749683 + -3.4
x = 4.044749683 + -3.4

Combine like terms: 4.044749683 + -3.4 = 0.644749683
x = 0.644749683

Simplifying
x = 0.644749683


Subproblem 2
x + 3.4 = -4.044749683

Simplifying
x + 3.4 = -4.044749683

Reorder the terms:
3.4 + x = -4.044749683

Solving
3.4 + x = -4.044749683

Solving for variable 'x'.

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

Add '-3.4' to each side of the equation.
3.4 + -3.4 + x = -4.044749683 + -3.4

Combine like terms: 3.4 + -3.4 = 0.0
0.0 + x = -4.044749683 + -3.4
x = -4.044749683 + -3.4

Combine like terms: -4.044749683 + -3.4 = -7.444749683
x = -7.444749683

Simplifying
x = -7.444749683


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.644749683, -7.444749683}
Solution
x = {0.644749683, -7.444749683}

See similar equations:

| F(X)=2x^3-5x^2-x+14F(4) | | 5x-15=30+2x | | 7x-4(2x-9)=50 | | (1/2x)-4=3-(1/3x) | | 23-2x=22 | | 9f+6g-4f-2g+2= | | 16x^2+8x+2=10 | | 5(x+6)=3(x-5) | | 3y+6=-18 | | -0.375h=-12 | | 36x+159= | | 5x-15=30+2 | | 2x+1y=78 | | -2.6h=-12 | | 8(x+4)=6(x-2) | | (5x+4)(3x+2)=(7x-1)(3x-5)+60x-51 | | 2(5+w)=94-w | | 1=7-3x | | 7p=7(4p+9) | | (5+2w)+w=94 | | x=(-8) | | 5m-2m+4m-6m= | | 4.7x-39=2.3x+9 | | 6(6x+6)=36x+36 | | 6ab-3ba= | | 5x^2-36x-108=0 | | 14k-70=42 | | 4x^2-10x-288=x^2-22x | | 2(x)+x=180-63 | | 2k-10=-42 | | x+(3x-10)=90 | | (7*3)-n=9 |

Equations solver categories