Solve the equation:
(x – 4)(x – 3) = 0
show your work and check your work.

Step-by-step explanation:

The given equation is

(x – 4)(x – 3) = 0

We would open the parenthesis by multiplying each term in the first parenthesis by each term in the second parentheses. It becomes

x^2 - 3x - 4x + 12 = 0

x^2 - 7x + 12

We would apply the method of factorization by looking for two numbers such that, when they are added or subtracted, the result would be -7x and when they are multiplied, the result would be 12x^2. The two numbers are -3x and - 4x. Therefore

x^2 -3x - 4x + 12 = 0

x(x - 3) - 4(x - 3) = 0

(x - 3)(x - 4) = 0

x - 3 = 0 or x - 4 = 0

x = 3 or x = 4

So let us check

if x = 3,

(3 – 4)(3 – 3) = 0

- 1×0 = 0

If x = 4

(4 – 4)(4 – 3) = 0

0×1 = 0

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)