(3x+2)(3x+5)-(3x+9)(3x-2)=x — step-by-step solution | Explain MAths

(3x+2)(3x+5)-(3x+9)(3x-2)=x

⚠ 3x is read as the product 3*x: for a power, write 3^x‖(3x+2)(3x+5)-(3x+9)(3x-2)=x is read as (3x+2)*(3x+5)-(3x+9)*(3x-2)=x: use (...)*(...) for multiplication, use (...)^(...) for a power

Let's solve in

ℝ

:

(3 x + 2) \cdot (3 x + 5) - (3 x + 9) \cdot (3 x - 2) = x

ℹ

(3 x + 2) \cdot (3 x + 5)

=

3 \cdot x \cdot 3 \cdot x

+ 3 x \cdot 5

+ 2 \cdot 3 x

+ 2 \cdot 5

‖

- (3 x + 9) \cdot (3 x - 2)

=

- (3 \cdot x \cdot 3 \cdot x

+ 3 x \cdot (-2)

+ 9 \cdot 3 x

+ 9 \cdot (-2))

(3 \cdot x \cdot 3 \cdot x

+ 3 x \cdot 5

+ 2 \cdot 3 x

+ 2 \cdot 5) - (3 \cdot x \cdot 3 \cdot x

+ 3 x \cdot (-2)

+ 9 \cdot 3 x

+ 9 \cdot (-2)) = x

ℹ

3 \cdot 3

=

9

‖

x \cdot x

=

x^{2}

‖

3 \cdot 5

=

15

‖

2 \cdot 3

=

6

‖

2 \cdot 5

=

10

‖

- (3 \cdot x \cdot 3 \cdot x

+ 3 x \cdot (-2)

+ 9 \cdot 3 x

+ 9 \cdot (-2))

=

- 3 \cdot x \cdot 3 \cdot x

- 3 x \cdot (-2)

- 9 \cdot 3 x

- 9 \cdot (-2)

9 x^{2}

+ 15 x

+ 6 x

+ 10

- 3 \cdot x \cdot 3 \cdot x

- 3 x \cdot (-2)

- 9 \cdot 3 x

- 9 \cdot (-2) = x

ℹ

15 x + 6 x

=

21 x

‖

3 \cdot 3

=

9

‖

x \cdot x

=

x^{2}

‖

-3 \cdot (-2)

=

6

‖

9 \cdot 3

=

27

‖

-9 \cdot (-2)

=

18

9 x^{2}

+ 21 x

+ 10

- 9 x^{2}

+ 6 x

- 27 x

+ 18 = x

ℹ

10 + 18

=

28

‖

9 x^{2} - 9 x^{2}

=

0

‖

21 x + 6 x - 27 x

=

0

0 + 0 + 28 = x

28 = x

0 = x - 28

▶Solution obtained:

x = 28