(3x-4)(4x-3)=(6x-4)(12x-5)

Simple and best practice solution for (3x-4)(4x-3)=(6x-4)(12x-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-4)(4x-3)=(6x-4)(12x-5) equation: 


Simplifying
(3x + -4)(4x + -3) = (6x + -4)(12x + -5)

Reorder the terms:
(-4 + 3x)(4x + -3) = (6x + -4)(12x + -5)

Reorder the terms:
(-4 + 3x)(-3 + 4x) = (6x + -4)(12x + -5)

Multiply (-4 + 3x) * (-3 + 4x)
(-4(-3 + 4x) + 3x * (-3 + 4x)) = (6x + -4)(12x + -5)
((-3 * -4 + 4x * -4) + 3x * (-3 + 4x)) = (6x + -4)(12x + -5)
((12 + -16x) + 3x * (-3 + 4x)) = (6x + -4)(12x + -5)
(12 + -16x + (-3 * 3x + 4x * 3x)) = (6x + -4)(12x + -5)
(12 + -16x + (-9x + 12x2)) = (6x + -4)(12x + -5)

Combine like terms: -16x + -9x = -25x
(12 + -25x + 12x2) = (6x + -4)(12x + -5)

Reorder the terms:
12 + -25x + 12x2 = (-4 + 6x)(12x + -5)

Reorder the terms:
12 + -25x + 12x2 = (-4 + 6x)(-5 + 12x)

Multiply (-4 + 6x) * (-5 + 12x)
12 + -25x + 12x2 = (-4(-5 + 12x) + 6x * (-5 + 12x))
12 + -25x + 12x2 = ((-5 * -4 + 12x * -4) + 6x * (-5 + 12x))
12 + -25x + 12x2 = ((20 + -48x) + 6x * (-5 + 12x))
12 + -25x + 12x2 = (20 + -48x + (-5 * 6x + 12x * 6x))
12 + -25x + 12x2 = (20 + -48x + (-30x + 72x2))

Combine like terms: -48x + -30x = -78x
12 + -25x + 12x2 = (20 + -78x + 72x2)

Solving
12 + -25x + 12x2 = 20 + -78x + 72x2

Solving for variable 'x'.

Reorder the terms:
12 + -20 + -25x + 78x + 12x2 + -72x2 = 20 + -78x + 72x2 + -20 + 78x + -72x2

Combine like terms: 12 + -20 = -8
-8 + -25x + 78x + 12x2 + -72x2 = 20 + -78x + 72x2 + -20 + 78x + -72x2

Combine like terms: -25x + 78x = 53x
-8 + 53x + 12x2 + -72x2 = 20 + -78x + 72x2 + -20 + 78x + -72x2

Combine like terms: 12x2 + -72x2 = -60x2
-8 + 53x + -60x2 = 20 + -78x + 72x2 + -20 + 78x + -72x2

Reorder the terms:
-8 + 53x + -60x2 = 20 + -20 + -78x + 78x + 72x2 + -72x2

Combine like terms: 20 + -20 = 0
-8 + 53x + -60x2 = 0 + -78x + 78x + 72x2 + -72x2
-8 + 53x + -60x2 = -78x + 78x + 72x2 + -72x2

Combine like terms: -78x + 78x = 0
-8 + 53x + -60x2 = 0 + 72x2 + -72x2
-8 + 53x + -60x2 = 72x2 + -72x2

Combine like terms: 72x2 + -72x2 = 0
-8 + 53x + -60x2 = 0

Begin completing the square.  Divide all terms by
-60 the coefficient of the squared term: 

Divide each side by '-60'.
0.1333333333 + -0.8833333333x + x2 = 0.0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + -0.8833333333x + -0.1333333333 + x2 = 0.0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + -0.8833333333x + x2 = 0.0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + -0.8833333333x + x2 = 0.0 + -0.1333333333
-0.8833333333x + x2 = 0.0 + -0.1333333333

Combine like terms: 0.0 + -0.1333333333 = -0.1333333333
-0.8833333333x + x2 = -0.1333333333

The x term is -0.8833333333x.  Take half its coefficient (-0.4416666667).
Square it (0.1950694445) and add it to both sides.

Add '0.1950694445' to each side of the equation.
-0.8833333333x + 0.1950694445 + x2 = -0.1333333333 + 0.1950694445

Reorder the terms:
0.1950694445 + -0.8833333333x + x2 = -0.1333333333 + 0.1950694445

Combine like terms: -0.1333333333 + 0.1950694445 = 0.0617361112
0.1950694445 + -0.8833333333x + x2 = 0.0617361112

Factor a perfect square on the left side:
(x + -0.4416666667)(x + -0.4416666667) = 0.0617361112

Calculate the square root of the right side: 0.248467525

Break this problem into two subproblems by setting 
(x + -0.4416666667) equal to 0.248467525 and -0.248467525.


Subproblem 1
x + -0.4416666667 = 0.248467525

Simplifying
x + -0.4416666667 = 0.248467525

Reorder the terms:
-0.4416666667 + x = 0.248467525

Solving
-0.4416666667 + x = 0.248467525

Solving for variable 'x'.

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

Add '0.4416666667' to each side of the equation.
-0.4416666667 + 0.4416666667 + x = 0.248467525 + 0.4416666667

Combine like terms: -0.4416666667 + 0.4416666667 = 0.0000000000
0.0000000000 + x = 0.248467525 + 0.4416666667
x = 0.248467525 + 0.4416666667

Combine like terms: 0.248467525 + 0.4416666667 = 0.6901341917
x = 0.6901341917

Simplifying
x = 0.6901341917


Subproblem 2
x + -0.4416666667 = -0.248467525

Simplifying
x + -0.4416666667 = -0.248467525

Reorder the terms:
-0.4416666667 + x = -0.248467525

Solving
-0.4416666667 + x = -0.248467525

Solving for variable 'x'.

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

Add '0.4416666667' to each side of the equation.
-0.4416666667 + 0.4416666667 + x = -0.248467525 + 0.4416666667

Combine like terms: -0.4416666667 + 0.4416666667 = 0.0000000000
0.0000000000 + x = -0.248467525 + 0.4416666667
x = -0.248467525 + 0.4416666667

Combine like terms: -0.248467525 + 0.4416666667 = 0.1931991417
x = 0.1931991417

Simplifying
x = 0.1931991417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6901341917, 0.1931991417}

See similar equations:

| -17x+10y-1=0 | | 3(3x-2)-6x= | | 4p+60=200 | | -5(v+9)=-7v-49 | | 4(e+2)=28 | | 3*-6+14= | | .5*5(x+2)=20 | | 5(p+7q-12)= | | x^4-14x^2*49=0 | | 4s+8=16 | | -2+40-8d=20 | | 3x+156=360 | | 20x^2-11x-42=0 | | 5.5=16t^2+t+30 | | -9+t=35 | | 5.5=16t^2+vot+30 | | 3(85-4x)+2x=105 | | 3(85-4x)+2x=105 | | 4y-1+90=180 | | 2d+40-8d=20 | | 1(1-5x)+8=-17+2x | | 60t+120=300 | | 60+120=300 | | x+4y=-0.5 | | x+4y=0.5 | | -12=d+5 | | 3(85-4y)+2x=105 | | -5n-4(-7-4n)=36+n | | x^2+2x+y-1=o | | (13k+10x)+(-8x-9k)=12k | | xy+2x+3y=7 | | X+7y=45 |

Equations solver categories