Question

find all solutions
36x²+12x=0

Answer 1

Answer:

x = -1/3 or 0

Step-by-step explanation:

Given equation:

• $36x^{2} + 12x = 0$

We can factor 12x on the L.H.S since 12x is divisible by 36x² and 12x.

$\implies 36x^{2} + 12x = 0$

$\implies 12x(3x + 1) = 0$

This can lead to two solutions. I have listed them below!

Solution 1:

Divide 12x on both sides to open the parentheses.

$\implies 12x(3x + 1) = 0$

$\implies \dfrac{12x(3x + 1)}{12} = \dfrac{0}{12}$

Note: zero divided by any non-zero number is 0.

$\implies \dfrac{12x(3x + 1)}{12} = \dfrac{0}{12}$

$\implies 3x + 1 = 0$

Isolate 3x on one side of the equation.

$\implies 3x + 1 = 0$

$\implies 3x = 0 - 1$

$\implies 3x = -1$

Divide 3 both sides to determine the value of x.

$\implies 3x = -1$

$\implies \dfrac{3x}{3} = \dfrac{-1}{3}$

$\implies \boxed{x = \dfrac{-1}{3}}$

Solution 2:

Divide (3x + 1) on both sides to isolate 12x.

$\implies 12x(3x + 1) = 0$

$\implies \dfrac{12x(3x + 1)}{(3x + 1)} = \dfrac{0}{(3x + 1)}$

Note: zero divided by any non-zero number is 0.

$\implies \dfrac{12x(3x + 1)}{(3x + 1)} = \dfrac{0}{(3x + 1)}$

$\implies 12x = 0$

Divide 12 both sides to determine the value of x.

$\implies 12x = 0$

$\implies \dfrac{12x}{12} = \dfrac{0}{12}$

$\implies \boxed{x = 0}$

Therefore, the solutions for x are -1/3 or 0.

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Answer 2

Answer:

x = 0  or  x = -1/3

Step-by-step explanation:

In the equation 36x²+12x=0 we have :

36x² = 6x × (6x)

12x = 2 × (6x)

This means that 6x is a common factor,so let’s factor :

36x²+12x=0

⇔ 6x × (6x) + 2 × (6x) = 0

⇔ 6x × (6x + 2) = 0

⇔ 6x = 0  or  6x + 2 = 0

⇔ x = 0  or  x = -2/6