2x-5(3x+5)+3x(x-6)=24

Simple and best practice solution for 2x-5(3x+5)+3x(x-6)=24 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 2x-5(3x+5)+3x(x-6)=24 equation:


Simplifying
2x + -5(3x + 5) + 3x(x + -6) = 24

Reorder the terms:
2x + -5(5 + 3x) + 3x(x + -6) = 24
2x + (5 * -5 + 3x * -5) + 3x(x + -6) = 24
2x + (-25 + -15x) + 3x(x + -6) = 24

Reorder the terms:
2x + -25 + -15x + 3x(-6 + x) = 24
2x + -25 + -15x + (-6 * 3x + x * 3x) = 24
2x + -25 + -15x + (-18x + 3x2) = 24

Reorder the terms:
-25 + 2x + -15x + -18x + 3x2 = 24

Combine like terms: 2x + -15x = -13x
-25 + -13x + -18x + 3x2 = 24

Combine like terms: -13x + -18x = -31x
-25 + -31x + 3x2 = 24

Solving
-25 + -31x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-25 + -24 + -31x + 3x2 = 24 + -24

Combine like terms: -25 + -24 = -49
-49 + -31x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-49 + -31x + 3x2 = 0

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

Divide each side by '3'.
-16.33333333 + -10.33333333x + x2 = 0

Move the constant term to the right:

Add '16.33333333' to each side of the equation.
-16.33333333 + -10.33333333x + 16.33333333 + x2 = 0 + 16.33333333

Reorder the terms:
-16.33333333 + 16.33333333 + -10.33333333x + x2 = 0 + 16.33333333

Combine like terms: -16.33333333 + 16.33333333 = 0.00000000
0.00000000 + -10.33333333x + x2 = 0 + 16.33333333
-10.33333333x + x2 = 0 + 16.33333333

Combine like terms: 0 + 16.33333333 = 16.33333333
-10.33333333x + x2 = 16.33333333

The x term is -10.33333333x.  Take half its coefficient (-5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
-10.33333333x + 26.69444443 + x2 = 16.33333333 + 26.69444443

Reorder the terms:
26.69444443 + -10.33333333x + x2 = 16.33333333 + 26.69444443

Combine like terms: 16.33333333 + 26.69444443 = 43.02777776
26.69444443 + -10.33333333x + x2 = 43.02777776

Factor a perfect square on the left side:
(x + -5.166666665)(x + -5.166666665) = 43.02777776

Calculate the square root of the right side: 6.559556217

Break this problem into two subproblems by setting 
(x + -5.166666665) equal to 6.559556217 and -6.559556217.

Subproblem 1

x + -5.166666665 = 6.559556217 Simplifying x + -5.166666665 = 6.559556217 Reorder the terms: -5.166666665 + x = 6.559556217 Solving -5.166666665 + x = 6.559556217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = 6.559556217 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = 6.559556217 + 5.166666665 x = 6.559556217 + 5.166666665 Combine like terms: 6.559556217 + 5.166666665 = 11.726222882 x = 11.726222882 Simplifying x = 11.726222882

Subproblem 2

x + -5.166666665 = -6.559556217 Simplifying x + -5.166666665 = -6.559556217 Reorder the terms: -5.166666665 + x = -6.559556217 Solving -5.166666665 + x = -6.559556217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = -6.559556217 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = -6.559556217 + 5.166666665 x = -6.559556217 + 5.166666665 Combine like terms: -6.559556217 + 5.166666665 = -1.392889552 x = -1.392889552 Simplifying x = -1.392889552

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.726222882, -1.392889552}

See similar equations:

| 1/4a=3 | | d+3=9d+11 | | 4+-1=13x-73 | | 7[6+8(6-x)+5]=9-5x | | y^4-21y^2-100=0 | | 4t^3-16t=0 | | 5d+2=7d+7 | | 6p+p1/2-1=0 | | 4y+2y=12 | | -5(s+9)+2s=-15 | | -5x+200=100 | | -2x+9=8x-21 | | 11x+26=5x+182 | | 3ax+16y=3 | | 4(x-3)+7x=-7(3-2x) | | 5x+4x-3+5x+4x-3= | | x-13x1/2+12=0 | | X^2=ln(7/8) | | -5(S+9)+25=-15 | | 7d+9=3d+1 | | 6+3-3+6+3-3= | | -2(-5-5v)=6(3v-1) | | 4(x+6)=5(2x) | | y^4+21y^2+100=0 | | -5(5+9)+25=-15 | | 190-5x=31x+22 | | 6x+3x-3+6x+3x-3= | | 6d+10=4d+3 | | y=ln(x+3) | | 6(2x-5)=4+2 | | ln(x^4)+ln(x^5)=6+ln(x^3) | | 6-8x=158-36x |

Equations solver categories