x*(x+5)=7*(x+5)

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Solution for x*(x+5)=7*(x+5) equation: 


Simplifying
x(x + 5) = 7(x + 5)

Reorder the terms:
x(5 + x) = 7(x + 5)
(5 * x + x * x) = 7(x + 5)
(5x + x2) = 7(x + 5)

Reorder the terms:
5x + x2 = 7(5 + x)
5x + x2 = (5 * 7 + x * 7)
5x + x2 = (35 + 7x)

Solving
5x + x2 = 35 + 7x

Solving for variable 'x'.

Reorder the terms:
-35 + 5x + -7x + x2 = 35 + 7x + -35 + -7x

Combine like terms: 5x + -7x = -2x
-35 + -2x + x2 = 35 + 7x + -35 + -7x

Reorder the terms:
-35 + -2x + x2 = 35 + -35 + 7x + -7x

Combine like terms: 35 + -35 = 0
-35 + -2x + x2 = 0 + 7x + -7x
-35 + -2x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-35 + -2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-5, 7}

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