# How to solve x: (x + 3)(x – 2) = 4(x – 1/4) ?

Welcome to my article x: (x + 3)(x – 2) = 4(x – 1/4). This question is taken from the simplification lesson.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
For complete information on how to solve this question x: (x + 3)(x – 2) = 4(x – 1/4), read and understand it carefully till the end.

Let us know how to solve this question x: (x + 3)(x – 2) = 4(x – 1/4).

First write the question on the page of the notebook

## x: (x + 3)(x – 2) = 4(x – 1/4)

write it like this,

\displaystyle (x+3)(x-2)=4(x-\frac{1}{4})

\displaystyle (x+3)(x-2)=4(\frac{{4x-1}}{4})

\displaystyle (x+3)(x-2)=\frac{4}{4}(4x-1)

\displaystyle (x+3)(x-2)=(4x-1)

\displaystyle x(x-2)+3(x-2)=(4x-1)

\displaystyle x\text{x}x-2\text{x}x+3\text{x}x-2\text{x3}=4x-1

\displaystyle {{x}^{2}}-2x+3x-6=4x-1

\displaystyle {{x}^{2}}-5x-6=4x-1

\displaystyle {{x}^{2}}-5x-6-4x+1=0

\displaystyle {{x}^{2}}-5x-4x+1-6=0

\displaystyle {{x}^{2}}-5x-4x-5=0

\displaystyle {{x}^{2}}-9x-5=0

To solve this question, we use these formulas,

\displaystyle x=\frac{{-b\pm \sqrt{{{{b}^{2}}-4ac}}}}{{2a}}

Here,
a = 1,
b =-9 ,
c = -5
Putting this value in the formula,

\displaystyle x=\frac{{-(-9)\pm \sqrt{{{{{(-9)}}^{2}}-4\text{x1x-5}}}}}{{2\text{x1}}}

\displaystyle x=\frac{{(9)\pm \sqrt{{(81)+20}}}}{{2}}

\displaystyle x=\frac{{(9)\pm \sqrt{{101}}}}{{2}}

And,

## x: (x + 3)(x – 2) = 4(x – 1/4)

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See the solution of more questions like this,

How to solve (x+4)(x-5)=3(x/3)+3 ?

We can solve these type of questions very easily in the following way:

First of all write like this,

\displaystyle (x+4(x-5)=3(\frac{x}{3})+3

\displaystyle x(x-5)+4(x-5)=3(\frac{x}{3})+3

\displaystyle {{x}^{2}}-5x+4x-5=x+3

\displaystyle {{x}^{2}}-5x+4x-x-5-3=0

\displaystyle {{x}^{2}}-6x+4x-8=0

\displaystyle {{x}^{2}}-2x-8=0

\displaystyle {{x}^{2}}-4x+2x-8=0

\displaystyle x(x-4)+2(x-4)=0

\displaystyle (x-4)(x+2)=0

If
x -4=0
So,