(ax+b)*(cx+d)=1

Simple and best practice solution for (ax+b)*(cx+d)=1 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 (ax+b)*(cx+d)=1 equation:


Simplifying
(ax + b)(cx + d) = 1

Multiply (ax + b) * (cx + d)
(ax(cx + d) + b(cx + d)) = 1
((cx * ax + d * ax) + b(cx + d)) = 1
((acx2 + adx) + b(cx + d)) = 1
(acx2 + adx + (cx * b + d * b)) = 1
(acx2 + adx + (bcx + bd)) = 1
(acx2 + adx + bcx + bd) = 1

Solving
acx2 + adx + bcx + bd = 1

Solving for variable 'a'.

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

Add '-1bcx' to each side of the equation.
acx2 + adx + bcx + -1bcx + bd = 1 + -1bcx

Combine like terms: bcx + -1bcx = 0
acx2 + adx + 0 + bd = 1 + -1bcx
acx2 + adx + bd = 1 + -1bcx

Add '-1bd' to each side of the equation.
acx2 + adx + bd + -1bd = 1 + -1bcx + -1bd

Combine like terms: bd + -1bd = 0
acx2 + adx + 0 = 1 + -1bcx + -1bd
acx2 + adx = 1 + -1bcx + -1bd

Reorder the terms:
-1 + acx2 + adx + bcx + bd = 1 + -1bcx + -1bd + -1 + bcx + bd

Reorder the terms:
-1 + acx2 + adx + bcx + bd = 1 + -1 + -1bcx + bcx + -1bd + bd

Combine like terms: 1 + -1 = 0
-1 + acx2 + adx + bcx + bd = 0 + -1bcx + bcx + -1bd + bd
-1 + acx2 + adx + bcx + bd = -1bcx + bcx + -1bd + bd

Combine like terms: -1bcx + bcx = 0
-1 + acx2 + adx + bcx + bd = 0 + -1bd + bd
-1 + acx2 + adx + bcx + bd = -1bd + bd

Combine like terms: -1bd + bd = 0
-1 + acx2 + adx + bcx + bd = 0

The solution to this equation could not be determined.

See similar equations:

| -4y+12=6y+12 | | 4(m-3)=24 | | 6+3x=.5(12+6x) | | A=18x | | y-8=-0.5(x+4) | | 10x+5-5x=25 | | x^4-15x^2-36=0 | | 3.00+2.00x=10 | | 1+7u=26 | | 1.00+3.00x=10 | | 7st-3st= | | 7y+2(y-5)+y= | | 2(1+4)+6*1=48 | | 20+4x=40+4y | | 5-10.6X=205.8 | | 35x+110=-45x^2 | | 60+60*o+1= | | 20x+2x^2=40x+2x^2 | | (3x-4y)(-2x+5y-6)= | | 36x^4+2x^2-8=0 | | 6x+2=x+2.6x+2 | | 45+1X=168 | | 5x-2+3x+4= | | -0.10(x-2)=0.16 | | 6.00+13x=97 | | X+0.23(26800)=1.23X | | X+0.23X=26800 | | X+0.23X=1.23X | | 24v^3x^4y^2+20v^6x^8=0 | | 25+50x=70+40y | | 3x-6=3+6 | | f(x)=-4x^2+5 |

Equations solver categories