(3x-2)(x+5)=5

Simple and best practice solution for (3x-2)(x+5)=5 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)(x+5)=5 equation:


Simplifying
(3x + -2)(x + 5) = 5

Reorder the terms:
(-2 + 3x)(x + 5) = 5

Reorder the terms:
(-2 + 3x)(5 + x) = 5

Multiply (-2 + 3x) * (5 + x)
(-2(5 + x) + 3x * (5 + x)) = 5
((5 * -2 + x * -2) + 3x * (5 + x)) = 5
((-10 + -2x) + 3x * (5 + x)) = 5
(-10 + -2x + (5 * 3x + x * 3x)) = 5
(-10 + -2x + (15x + 3x2)) = 5

Combine like terms: -2x + 15x = 13x
(-10 + 13x + 3x2) = 5

Solving
-10 + 13x + 3x2 = 5

Solving for variable 'x'.

Reorder the terms:
-10 + -5 + 13x + 3x2 = 5 + -5

Combine like terms: -10 + -5 = -15
-15 + 13x + 3x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-15 + 13x + 3x2 = 0

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

Divide each side by '3'.
-5 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 4.333333333x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 4.333333333x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 4.333333333x + x2 = 0 + 5
4.333333333x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
4.333333333x + x2 = 5

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 5 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 5 + 4.694444446

Combine like terms: 5 + 4.694444446 = 9.694444446
4.694444446 + 4.333333333x + x2 = 9.694444446

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 9.694444446

Calculate the square root of the right side: 3.113590282

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 3.113590282 and -3.113590282.

Subproblem 1

x + 2.166666667 = 3.113590282 Simplifying x + 2.166666667 = 3.113590282 Reorder the terms: 2.166666667 + x = 3.113590282 Solving 2.166666667 + x = 3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 3.113590282 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 3.113590282 + -2.166666667 x = 3.113590282 + -2.166666667 Combine like terms: 3.113590282 + -2.166666667 = 0.946923615 x = 0.946923615 Simplifying x = 0.946923615

Subproblem 2

x + 2.166666667 = -3.113590282 Simplifying x + 2.166666667 = -3.113590282 Reorder the terms: 2.166666667 + x = -3.113590282 Solving 2.166666667 + x = -3.113590282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -3.113590282 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -3.113590282 + -2.166666667 x = -3.113590282 + -2.166666667 Combine like terms: -3.113590282 + -2.166666667 = -5.280256949 x = -5.280256949 Simplifying x = -5.280256949

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.946923615, -5.280256949}

See similar equations:

| 2n=45 | | 9x-10=3x+25 | | 3s^2+13s-10=0 | | 2(13+x)=41x | | 18=-6/7y | | 8x+9=10x-1 | | 2+7+x=18 | | 4x-6+2x-2=-20 | | 4x-6+2x-2=-20I | | -19(15x+17)= | | 1x(4x-20)=180 | | 4g^2+43g-11=0 | | f^2+43f=0 | | -6=Y/10-3 | | 4/3=6/a | | 1.9=3y+14.8 | | s^2-20s+19=0 | | 4(3t-2)=32 | | h^2+48h=0 | | 2x+50*2=242 | | 1/3=x-7/6 | | 3n+2.5=7.3 | | k^2+41k=0 | | 4-2y=24 | | f^2-9f-22=0 | | -1x^2+2x+6=0 | | 6(h+3)=3(h+11) | | y+2(4)=4 | | 5/x-4=3/2 | | y+2(3)=4 | | 6(2+6x)=2-x | | q^2-26q+25=0 |

Equations solver categories