Albert Teen
powered by
Albert logo


Solving Equations by Factorising

Solving Equations by Factorising

Solving Equations by Factorising

Factorising is the first step in solving an equation, which we can use to find the value of an unknown quantity.

Factorising can be the first step to solving a quadratic equation to find the value of an unknown.

When solving equations by factorising, we often end up with two sets of brackets equal to zero. This means that we find two solutions for xx.

Let's start with a quadratic: x27x+12=0x^2-7x+12=0


First of all, we need to factorise the equation

We can factorise by finding a pair of factors which multiply to make 1212, and add together to give 7-7.


Factorise x27x+12=0x^2-7x+12=0


We can factorise to form (x3)(x4)=0(x - 3)(x - 4) = 0

This means that we have two solutions for xx, one in each bracket. So, we effectively have x3=0x-3=0 and x4=0x-4=0


For x3=0x-3=0, subtract 3 from both sides

x 3=0+3x\space\cancel{-3}=0+3 so x=3x=3


If x4=0x-4=0, what is xx?


x=4x=4 when x4=0x-4=0

Therefore, there are two solutions to the equation. x=3x=3 and x=4x=4.

What are the solutions to the equation: (x5)(x6)=0(x - 5)(x - 6) = 0?

Find the two solutions to the equation: (x4)(x+7)=0(x - 4)(x + 7) = 0

You may have to do some more work to find the values of xx in some cases.

Let's try solving (2x+3)(3x1)=0(2x + 3)(3x - 1) = 0


We can treat this as two equations

We need to solve 2x+3=02x+3=0 and 3x1=03x-1=0. This means that we will have two different solutions for xx.


Solve the left bracket 2x+3=02x+3=0


Solve the right bracket 3x1=03x-1=0


There we go! You've solved it

x=32x=-\dfrac{3}{2} and x=13x=\dfrac{1}{3}


Always give these answers as exact fractions where possible

Don't give mixed numbers!

Solve (2x+4)(3x12)=0(2x + 4)(3x - 12) = 0

What are the solutions to the equation: (5x+3)(7x24)=0(5x + 3)(7x - 24) = 0?