Who can help me solve these equations showing all the steps?

Question

x ^2 + x = 0

n ^2 = 5n

7x ^2 = 3x

Answer 1

x ^2 + x = 0

x (x+1) = 0, so x = 0 or x = -1

n^2 -5n = 0

n(n-5) = 0, so n = 0 or n = 5

7x^2 - 3x = 0

x (7x -3) = 0, so x = 0 or 7x - 3 = 0 ie: x = 3/7

x ^2 - 8x = 0

x ( x -8 ) = 0, so x = 0 or x = 8

Answer 2

PROBLEM 1:

Factor out an x:

x(x + 1) = 0

If two things multiply to be zero, then one of them must be zero.

x = 0

or

x + 1 = 0

x = -1

Answer:

x = 0 or x = -1

PROBLEM 2:

Get everything on one side by subtracting 5n from both:

n² - 5n = 0

Factor out n:

n(n - 5) = 0

Again:

n = 0

or

n - 5 = 0

Answer:

n = 0 or n = 5

PROBLEM 3:

7x² - 3x = 0

x(7x - 3) = 0

x = 0

or

7x - 3 = 0

7x = 3

x = 3/7

Answer:

x = 0 or x = 3/7

PROBLEM 4:

x² - 8x = 0

x(x - 8) = 0

x = 0

or

x - 8 = 0

Answer:

x = 0 or x = 8

Answer 3

x^2 + x = 0   <==== factor:

x(x + 1) = 0   <==== set factors equal to 0 and solve

x = 0 or x = -1

n^2 = 5n   <==== collect terms and put in standard form

n^2 - 5n = 0   <==== factor and continue as above

n(n - 5) = 0

n = 0 or n = 5

7x^2 = 3x    <==== same steps as previous problem

7x^2 - 3x = 0

x(7x - 3) = 0

x = 0 or x = 3/7

x^2 - 8x = 0

x(x - 8) = 0

x = 0 or x = 8

Answer 4

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