3x(4x-5)-10+5=5x(x-4)+4

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


Simplifying
3x(4x + -5) + -10 + 5 = 5x(x + -4) + 4

Reorder the terms:
3x(-5 + 4x) + -10 + 5 = 5x(x + -4) + 4
(-5 * 3x + 4x * 3x) + -10 + 5 = 5x(x + -4) + 4
(-15x + 12x2) + -10 + 5 = 5x(x + -4) + 4

Reorder the terms:
-10 + 5 + -15x + 12x2 = 5x(x + -4) + 4

Combine like terms: -10 + 5 = -5
-5 + -15x + 12x2 = 5x(x + -4) + 4

Reorder the terms:
-5 + -15x + 12x2 = 5x(-4 + x) + 4
-5 + -15x + 12x2 = (-4 * 5x + x * 5x) + 4
-5 + -15x + 12x2 = (-20x + 5x2) + 4

Reorder the terms:
-5 + -15x + 12x2 = 4 + -20x + 5x2

Solving
-5 + -15x + 12x2 = 4 + -20x + 5x2

Solving for variable 'x'.

Reorder the terms:
-5 + -4 + -15x + 20x + 12x2 + -5x2 = 4 + -20x + 5x2 + -4 + 20x + -5x2

Combine like terms: -5 + -4 = -9
-9 + -15x + 20x + 12x2 + -5x2 = 4 + -20x + 5x2 + -4 + 20x + -5x2

Combine like terms: -15x + 20x = 5x
-9 + 5x + 12x2 + -5x2 = 4 + -20x + 5x2 + -4 + 20x + -5x2

Combine like terms: 12x2 + -5x2 = 7x2
-9 + 5x + 7x2 = 4 + -20x + 5x2 + -4 + 20x + -5x2

Reorder the terms:
-9 + 5x + 7x2 = 4 + -4 + -20x + 20x + 5x2 + -5x2

Combine like terms: 4 + -4 = 0
-9 + 5x + 7x2 = 0 + -20x + 20x + 5x2 + -5x2
-9 + 5x + 7x2 = -20x + 20x + 5x2 + -5x2

Combine like terms: -20x + 20x = 0
-9 + 5x + 7x2 = 0 + 5x2 + -5x2
-9 + 5x + 7x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-9 + 5x + 7x2 = 0

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

Divide each side by '7'.
-1.285714286 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + 0.7142857143x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + 0.7142857143x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + 0.7142857143x + x2 = 0 + 1.285714286
0.7142857143x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
0.7142857143x + x2 = 1.285714286

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = 1.285714286 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = 1.285714286 + 0.1275510204

Combine like terms: 1.285714286 + 0.1275510204 = 1.4132653064
0.1275510204 + 0.7142857143x + x2 = 1.4132653064

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 1.4132653064

Calculate the square root of the right side: 1.188808356

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 1.188808356 and -1.188808356.

Subproblem 1

x + 0.3571428572 = 1.188808356 Simplifying x + 0.3571428572 = 1.188808356 Reorder the terms: 0.3571428572 + x = 1.188808356 Solving 0.3571428572 + x = 1.188808356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 1.188808356 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 1.188808356 + -0.3571428572 x = 1.188808356 + -0.3571428572 Combine like terms: 1.188808356 + -0.3571428572 = 0.8316654988 x = 0.8316654988 Simplifying x = 0.8316654988

Subproblem 2

x + 0.3571428572 = -1.188808356 Simplifying x + 0.3571428572 = -1.188808356 Reorder the terms: 0.3571428572 + x = -1.188808356 Solving 0.3571428572 + x = -1.188808356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -1.188808356 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -1.188808356 + -0.3571428572 x = -1.188808356 + -0.3571428572 Combine like terms: -1.188808356 + -0.3571428572 = -1.5459512132 x = -1.5459512132 Simplifying x = -1.5459512132

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8316654988, -1.5459512132}

See similar equations:

| 7-5/7=9 | | logb(x-1)=2logb(x-1) | | 4x+9=7x+0 | | sine(x)=3cos(x) | | 22x-1/2x=200 | | 9+6x=7x+2 | | 2x-7=-x+17 | | 3/x-12=15/x | | 460+y=12x | | 3*(4x-5)-10+5=5*(x-4)+4 | | 5x-10=12-6x | | (5x)/x=(8x^3)/x^2 | | Y=x^2+-8x | | -83=-6x-3x+7 | | 1/2x+5=x+8 | | 5d+6(5d-1)-7= | | 4+2x-2=6x+2-3x | | 8+4x+2x=44 | | 6x+1=1-6x | | 2x^2-50x+500=0 | | (n^2-16)=0 | | 5x^2-50x=-85 | | -6x+6=5-5x | | 0.2x-lnx=0 | | 5-6p+8p=3p+7 | | (2x^2-2)(2x-2)= | | F(8)=8x-78+7x^2 | | 3x-5=5(x-1) | | -6x+7=-38+3x | | 12x^2-4ax-4bx+ab=0forx | | 20x+5-20=21x+4 | | Ln(x+6)+ln(x+4)=ln(x+5) |

Equations solver categories