3x^2+63x+120=

Simple and best practice solution for 3x^2+63x+120= 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+63x+120= equation: 


Simplifying
3x2 + 63x + 120 = 0

Reorder the terms:
120 + 63x + 3x2 = 0

Solving
120 + 63x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(40 + 21x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(40 + 21x + x2)' equal to zero and attempt to solve:

Simplifying
40 + 21x + x2 = 0

Solving
40 + 21x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 21x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 21x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 21x + x2 = 0 + -40
21x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
21x + x2 = -40

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = -40 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -40 + 110.25

Combine like terms: -40 + 110.25 = 70.25
110.25 + 21x + x2 = 70.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x + 10.5) equal to 8.381527307 and -8.381527307.


Subproblem 1
x + 10.5 = 8.381527307

Simplifying
x + 10.5 = 8.381527307

Reorder the terms:
10.5 + x = 8.381527307

Solving
10.5 + x = 8.381527307

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 8.381527307 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 8.381527307 + -10.5
x = 8.381527307 + -10.5

Combine like terms: 8.381527307 + -10.5 = -2.118472693
x = -2.118472693

Simplifying
x = -2.118472693


Subproblem 2
x + 10.5 = -8.381527307

Simplifying
x + 10.5 = -8.381527307

Reorder the terms:
10.5 + x = -8.381527307

Solving
10.5 + x = -8.381527307

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -8.381527307 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -8.381527307 + -10.5
x = -8.381527307 + -10.5

Combine like terms: -8.381527307 + -10.5 = -18.881527307
x = -18.881527307

Simplifying
x = -18.881527307


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.118472693, -18.881527307}
Solution
x = {-2.118472693, -18.881527307}

See similar equations:

| 12t=-36 | | 32.68=w-29 | | -18=-2(1-2p) | | 14+v=-8(2v-6) | | -4(x+5)=16 | | 6x-5=4x+43 | | 5+14=19 | | 4m-1=23 | | 8(4m-4)=-32+5m | | -5b-10=-5(6b-8) | | 55=2x+5x+6 | | 2(3-m)-2(4m-5)=-4+5m+1+4m | | -3(5x+1)=-6 | | m(x)+n(x)=p | | 2(c+4)=3(c-2) | | 0.14y+.06(y+2000)=1320 | | x=-2y+14 | | -2(3+8n)=-24-7n | | 6=4t-3t-2 | | (3x+2)2+8=9 | | 4(3-2x)+2(x+1)=-7 | | -7(2x+3)=-7 | | 27.95+q=12 | | -38-8x=6(1-5x) | | 6x-5=4x-43 | | 3-4=5(a-3) | | 4(2y-7)+4=9 | | x+6(0)=0 | | r-15.8=24.6 | | 5.3x-2.58=3.18-4.3x | | 0+6y=0 | | 4(9+5x)=196 |

Equations solver categories