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1. x =0; x = -7

2. x = -3; x = 10

3. x = -5; x = -4

Step-by-step explanation:

(1). 6x² + 42x = 0

6x (x + 7) = 0

6x = 0. OR. x + 7 = 0

x = 0/6. x = 0 - 7

x = 0. x = -7

x = 0

x = -7

(2). x² - 7x - 30 = 0

The factors here are (3, -10)

x² - 10x + 3x - 30 = 0

x ( x - 10) + 3 ( x - 10) = 0

(x + 3) ( x - 10) = 0

x + 3 = 0 OR. x - 10 = 0

x = 0-3. x = 0 + 10

x = -3. x = 10

x = -3

x = 10

(3). x² + 9x + 20 = 0

The factors are ( 4, 5)

x² + 4x + 5x + 20 = 0

x ( x + 4) + 5 ( x + 4) = 0

(x + 5) (x + 4) = 0

x + 5 = 0 . OR. x + 4 = 0

x = 0-5. x = 0 - 4

x = -5. x = -4

x = -5

x = -4

Step-by-step explanation:

1) 6x² + 42x

6x is common to both terms. Therefore, it becomes

6x(x + 7)

2) x² - 7x - 30

We would find two numbers such that their sum or difference is -7x and their product is - 30x².

The two numbers are 3x and -10x. It becomes

x² + 3x - 10x - 30

x(x + 3) - 10(x + 3)

(x + 3)(x - 10)

3) x² + 9x + 20

We would find two numbers such that their sum or difference is 9x and their product is 20x².

The two numbers are 4x and 5x. It becomes

x² + 4x + 5x + 20

x(x + 4) + 5(x + 4)

(x + 4)(x + 5)

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