-3x^2-9x+15=0

Simple and best practice solution for -3x^2-9x+15=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 -3x^2-9x+15=0 equation: 


Simplifying
-3x2 + -9x + 15 = 0

Reorder the terms:
15 + -9x + -3x2 = 0

Solving
15 + -9x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -3x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + -3x + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -3x + -1x2 = 0

Solving
5 + -3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + 3x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 3x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3x + x2 = 0 + 5
3x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
3x + x2 = 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 = 5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + 3x + x2 = 7.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
x + 1.5 = 2.692582404

Simplifying
x + 1.5 = 2.692582404

Reorder the terms:
1.5 + x = 2.692582404

Solving
1.5 + x = 2.692582404

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 = 2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.692582404 + -1.5
x = 2.692582404 + -1.5

Combine like terms: 2.692582404 + -1.5 = 1.192582404
x = 1.192582404

Simplifying
x = 1.192582404


Subproblem 2
x + 1.5 = -2.692582404

Simplifying
x + 1.5 = -2.692582404

Reorder the terms:
1.5 + x = -2.692582404

Solving
1.5 + x = -2.692582404

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 = -2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.692582404 + -1.5
x = -2.692582404 + -1.5

Combine like terms: -2.692582404 + -1.5 = -4.192582404
x = -4.192582404

Simplifying
x = -4.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.192582404, -4.192582404}
Solution
x = {1.192582404, -4.192582404}

See similar equations:

| y+2x-10=0 | | 3(x-4)+5=25 | | 4(x-2)+8(x-4)=8 | | 5p(p+2)=0 | | x-2y+10=0 | | 158x+5947=6 | | xy=13599273702913 | | 5(7-x)=-5 | | (2k-1)x^2+2kx-k=0 | | 2ln(2x-1)-10=0 | | 9-4x=9+3x | | 2f+1=3f-1.5 | | 2b+7=5b-2 | | 35y+1=56 | | 7[25-m]-2m=2[3m-25] | | y=1.5x+7.7 | | -5u-20=3(u-4) | | -2(u+3)=6u+10 | | 0=1829x-3 | | 8y+22=-2(y+9) | | 6x-2=3x+5 | | 3(t+4)=33 | | -7(4+5x)=7 | | 1-2356x=22 | | 3(a-2)=9 | | 16x^2-9=10 | | 7(a-2)=9 | | 2x^3-9x^2+14x-10=0 | | 6x+20=14x-17 | | x^4-2x^3-12x^2-13x-15=0 | | 7(x+5)=33 | | 9y=5y+3 |

Equations solver categories