3x(4x-11)+5x(7-2x)=16-3x(3x-10)

Simple and best practice solution for 3x(4x-11)+5x(7-2x)=16-3x(3x-10) 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(4x-11)+5x(7-2x)=16-3x(3x-10) equation: 


Simplifying
3x(4x + -11) + 5x(7 + -2x) = 16 + -3x(3x + -10)

Reorder the terms:
3x(-11 + 4x) + 5x(7 + -2x) = 16 + -3x(3x + -10)
(-11 * 3x + 4x * 3x) + 5x(7 + -2x) = 16 + -3x(3x + -10)
(-33x + 12x2) + 5x(7 + -2x) = 16 + -3x(3x + -10)
-33x + 12x2 + (7 * 5x + -2x * 5x) = 16 + -3x(3x + -10)
-33x + 12x2 + (35x + -10x2) = 16 + -3x(3x + -10)

Reorder the terms:
-33x + 35x + 12x2 + -10x2 = 16 + -3x(3x + -10)

Combine like terms: -33x + 35x = 2x
2x + 12x2 + -10x2 = 16 + -3x(3x + -10)

Combine like terms: 12x2 + -10x2 = 2x2
2x + 2x2 = 16 + -3x(3x + -10)

Reorder the terms:
2x + 2x2 = 16 + -3x(-10 + 3x)
2x + 2x2 = 16 + (-10 * -3x + 3x * -3x)
2x + 2x2 = 16 + (30x + -9x2)

Solving
2x + 2x2 = 16 + 30x + -9x2

Solving for variable 'x'.

Reorder the terms:
-16 + 2x + -30x + 2x2 + 9x2 = 16 + 30x + -9x2 + -16 + -30x + 9x2

Combine like terms: 2x + -30x = -28x
-16 + -28x + 2x2 + 9x2 = 16 + 30x + -9x2 + -16 + -30x + 9x2

Combine like terms: 2x2 + 9x2 = 11x2
-16 + -28x + 11x2 = 16 + 30x + -9x2 + -16 + -30x + 9x2

Reorder the terms:
-16 + -28x + 11x2 = 16 + -16 + 30x + -30x + -9x2 + 9x2

Combine like terms: 16 + -16 = 0
-16 + -28x + 11x2 = 0 + 30x + -30x + -9x2 + 9x2
-16 + -28x + 11x2 = 30x + -30x + -9x2 + 9x2

Combine like terms: 30x + -30x = 0
-16 + -28x + 11x2 = 0 + -9x2 + 9x2
-16 + -28x + 11x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-16 + -28x + 11x2 = 0

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

Divide each side by '11'.
-1.454545455 + -2.545454545x + x2 = 0

Move the constant term to the right:

Add '1.454545455' to each side of the equation.
-1.454545455 + -2.545454545x + 1.454545455 + x2 = 0 + 1.454545455

Reorder the terms:
-1.454545455 + 1.454545455 + -2.545454545x + x2 = 0 + 1.454545455

Combine like terms: -1.454545455 + 1.454545455 = 0.000000000
0.000000000 + -2.545454545x + x2 = 0 + 1.454545455
-2.545454545x + x2 = 0 + 1.454545455

Combine like terms: 0 + 1.454545455 = 1.454545455
-2.545454545x + x2 = 1.454545455

The x term is -2.545454545x.  Take half its coefficient (-1.272727273).
Square it (1.619834711) and add it to both sides.

Add '1.619834711' to each side of the equation.
-2.545454545x + 1.619834711 + x2 = 1.454545455 + 1.619834711

Reorder the terms:
1.619834711 + -2.545454545x + x2 = 1.454545455 + 1.619834711

Combine like terms: 1.454545455 + 1.619834711 = 3.074380166
1.619834711 + -2.545454545x + x2 = 3.074380166

Factor a perfect square on the left side:
(x + -1.272727273)(x + -1.272727273) = 3.074380166

Calculate the square root of the right side: 1.753391048

Break this problem into two subproblems by setting 
(x + -1.272727273) equal to 1.753391048 and -1.753391048.


Subproblem 1
x + -1.272727273 = 1.753391048

Simplifying
x + -1.272727273 = 1.753391048

Reorder the terms:
-1.272727273 + x = 1.753391048

Solving
-1.272727273 + x = 1.753391048

Solving for variable 'x'.

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

Add '1.272727273' to each side of the equation.
-1.272727273 + 1.272727273 + x = 1.753391048 + 1.272727273

Combine like terms: -1.272727273 + 1.272727273 = 0.000000000
0.000000000 + x = 1.753391048 + 1.272727273
x = 1.753391048 + 1.272727273

Combine like terms: 1.753391048 + 1.272727273 = 3.026118321
x = 3.026118321

Simplifying
x = 3.026118321


Subproblem 2
x + -1.272727273 = -1.753391048

Simplifying
x + -1.272727273 = -1.753391048

Reorder the terms:
-1.272727273 + x = -1.753391048

Solving
-1.272727273 + x = -1.753391048

Solving for variable 'x'.

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

Add '1.272727273' to each side of the equation.
-1.272727273 + 1.272727273 + x = -1.753391048 + 1.272727273

Combine like terms: -1.272727273 + 1.272727273 = 0.000000000
0.000000000 + x = -1.753391048 + 1.272727273
x = -1.753391048 + 1.272727273

Combine like terms: -1.753391048 + 1.272727273 = -0.480663775
x = -0.480663775

Simplifying
x = -0.480663775


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.026118321, -0.480663775}

See similar equations:

| 2(8x+13)=-2(8x-25) | | -20+7x=20-3x | | 45=-3-15x+3x | | 5+2x=6+x | | 2(x-1)=4x+8 | | 3x-5=15-2x | | 5+8-2x=15-3x+1 | | 8x-8=3x-7 | | 7m-8=3m+12 | | 5p-16=14 | | 5p-16=4 | | 2(x+8)=98 | | 14x=172 | | 4x+12=76-4x | | 6+8x=90+x | | 3x-3=13x-93 | | 4x+20=11x-64 | | 4(2t-1)=24 | | 5y-12=35x | | -5(3-q)+4=5q-11 | | 20x^2-19x=0 | | 0=-76+70t-16(t*t) | | g-7fh=9 | | (x*x)+5x-84=0 | | 12-x-12(x*x)=0 | | 3a-(-1)=-5 | | 7x-3=10x+15 | | x-0.1x+0.07(x-0.1x)=69.62 | | 12(x*x)+x-12=0 | | b(-2)-10=-2 | | 8+4x=-10+x | | bx-10=-2 |

Equations solver categories