(x+3)*(x+2)=120

Simple and best practice solution for (x+3)*(x+2)=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 (x+3)*(x+2)=120 equation:


Simplifying
(x + 3)(x + 2) = 120

Reorder the terms:
(3 + x)(x + 2) = 120

Reorder the terms:
(3 + x)(2 + x) = 120

Multiply (3 + x) * (2 + x)
(3(2 + x) + x(2 + x)) = 120
((2 * 3 + x * 3) + x(2 + x)) = 120
((6 + 3x) + x(2 + x)) = 120
(6 + 3x + (2 * x + x * x)) = 120
(6 + 3x + (2x + x2)) = 120

Combine like terms: 3x + 2x = 5x
(6 + 5x + x2) = 120

Solving
6 + 5x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
6 + -120 + 5x + x2 = 120 + -120

Combine like terms: 6 + -120 = -114
-114 + 5x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-114 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '114' to each side of the equation.
-114 + 5x + 114 + x2 = 0 + 114

Reorder the terms:
-114 + 114 + 5x + x2 = 0 + 114

Combine like terms: -114 + 114 = 0
0 + 5x + x2 = 0 + 114
5x + x2 = 0 + 114

Combine like terms: 0 + 114 = 114
5x + x2 = 114

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 114 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 114 + 6.25

Combine like terms: 114 + 6.25 = 120.25
6.25 + 5x + x2 = 120.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.9658561 and -10.9658561.

Subproblem 1

x + 2.5 = 10.9658561 Simplifying x + 2.5 = 10.9658561 Reorder the terms: 2.5 + x = 10.9658561 Solving 2.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.9658561 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.9658561 + -2.5 x = 10.9658561 + -2.5 Combine like terms: 10.9658561 + -2.5 = 8.4658561 x = 8.4658561 Simplifying x = 8.4658561

Subproblem 2

x + 2.5 = -10.9658561 Simplifying x + 2.5 = -10.9658561 Reorder the terms: 2.5 + x = -10.9658561 Solving 2.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.9658561 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.9658561 + -2.5 x = -10.9658561 + -2.5 Combine like terms: -10.9658561 + -2.5 = -13.4658561 x = -13.4658561 Simplifying x = -13.4658561

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.4658561, -13.4658561}

See similar equations:

| 1.2m=1(2m-12) | | a=10.0-2.0/3.0 | | 4x-3=x-4 | | (3/8)a+5=(1/5) | | 2w-12w=70 | | a=2.0-10.0/3.0 | | 4x^4-12x^3+13x^2-6x-8=0 | | 12x^2-46x+40=0 | | 4p-5+p=-7+5p+2 | | (-7/20)b+2=(8/5) | | 4p-5+p=-7+5x+2 | | 20.4=s/2.5 | | x^2+1x=1x+1 | | -6n+13=-5n-1 | | x^8-18x^4+32=0 | | 3n-7=6(2n-2) | | 1/2x=5/4 | | x+115+70=180 | | 3t+7=5+t+9 | | -1p=1p-4 | | (7/8)w=-16 | | 1/5x=7/5 | | X^2+4x+13=25 | | 7y-0y=-9-13 | | X+X+3+X+X+3=30 | | 26=6t-19t | | (3x+9)=324 | | 3f+120=20-1f | | y+2/4=-5 | | -k-273=c | | x^4-9x^3+22x^2-9x+1=0 | | 6=-4-5x |

Equations solver categories