3x(5-2x)+8=2x(3x-7)+x

Simple and best practice solution for 3x(5-2x)+8=2x(3x-7)+x 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(5-2x)+8=2x(3x-7)+x equation: 


Simplifying
3x(5 + -2x) + 8 = 2x(3x + -7) + x
(5 * 3x + -2x * 3x) + 8 = 2x(3x + -7) + x
(15x + -6x2) + 8 = 2x(3x + -7) + x

Reorder the terms:
8 + 15x + -6x2 = 2x(3x + -7) + x

Reorder the terms:
8 + 15x + -6x2 = 2x(-7 + 3x) + x
8 + 15x + -6x2 = (-7 * 2x + 3x * 2x) + x
8 + 15x + -6x2 = (-14x + 6x2) + x

Reorder the terms:
8 + 15x + -6x2 = -14x + x + 6x2

Combine like terms: -14x + x = -13x
8 + 15x + -6x2 = -13x + 6x2

Solving
8 + 15x + -6x2 = -13x + 6x2

Solving for variable 'x'.

Reorder the terms:
8 + 15x + 13x + -6x2 + -6x2 = -13x + 6x2 + 13x + -6x2

Combine like terms: 15x + 13x = 28x
8 + 28x + -6x2 + -6x2 = -13x + 6x2 + 13x + -6x2

Combine like terms: -6x2 + -6x2 = -12x2
8 + 28x + -12x2 = -13x + 6x2 + 13x + -6x2

Reorder the terms:
8 + 28x + -12x2 = -13x + 13x + 6x2 + -6x2

Combine like terms: -13x + 13x = 0
8 + 28x + -12x2 = 0 + 6x2 + -6x2
8 + 28x + -12x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
8 + 28x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 7x + -3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(2 + 7x + -3x2)' equal to zero and attempt to solve:

Simplifying
2 + 7x + -3x2 = 0

Solving
2 + 7x + -3x2 = 0

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

Divide each side by '-3'.
-0.6666666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -2.333333333x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -2.333333333x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -2.333333333x + x2 = 0 + 0.6666666667
-2.333333333x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-2.333333333x + x2 = 0.6666666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 0.6666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 0.6666666667 + 1.361111112

Combine like terms: 0.6666666667 + 1.361111112 = 2.0277777787
1.361111112 + -2.333333333x + x2 = 2.0277777787

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 2.0277777787

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.424000625 and -1.424000625.


Subproblem 1
x + -1.166666667 = 1.424000625

Simplifying
x + -1.166666667 = 1.424000625

Reorder the terms:
-1.166666667 + x = 1.424000625

Solving
-1.166666667 + x = 1.424000625

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 1.424000625 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 1.424000625 + 1.166666667
x = 1.424000625 + 1.166666667

Combine like terms: 1.424000625 + 1.166666667 = 2.590667292
x = 2.590667292

Simplifying
x = 2.590667292


Subproblem 2
x + -1.166666667 = -1.424000625

Simplifying
x + -1.166666667 = -1.424000625

Reorder the terms:
-1.166666667 + x = -1.424000625

Solving
-1.166666667 + x = -1.424000625

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -1.424000625 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -1.424000625 + 1.166666667
x = -1.424000625 + 1.166666667

Combine like terms: -1.424000625 + 1.166666667 = -0.257333958
x = -0.257333958

Simplifying
x = -0.257333958


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.590667292, -0.257333958}
Solution
x = {2.590667292, -0.257333958}

See similar equations:

| 35=4(9b+6) | | -5tx=9 | | -6+y=-1 | | x^2-14=159 | | 6h-8-9h=29 | | 6k+8k=30 | | x^2+5=900 | | y=237(.75)*2 | | x=5x-9 | | -5+7(1+8y)=-28 | | -9x-12y=9 | | y=-10+5 | | 2h+6=144 | | y=237(.75) | | -16=-2+3(v+6) | | 36x+4y+32=0 | | 3x+-4+107=180 | | 128=-4(-5x+8) | | 10-4f+f= | | 2x+(x+10)+3x=142 | | 9y=75+6 | | h(t)=6t^2-2t | | 6y+2(y-8)=5(y+1)-2 | | 0.3x=x-22 | | 9y=-2 | | 3x^3-x^2-24x=0 | | 5p+35q= | | -6(-3+x)=42 | | 4b-4-8b=13 | | x^2-13=102 | | 10-a+2a= | | x^2+6=400 |

Equations solver categories