x(x-7)=5x+13

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Solution for x(x-7)=5x+13 equation: 


Simplifying
x(x + -7) = 5x + 13

Reorder the terms:
x(-7 + x) = 5x + 13
(-7 * x + x * x) = 5x + 13
(-7x + x2) = 5x + 13

Reorder the terms:
-7x + x2 = 13 + 5x

Solving
-7x + x2 = 13 + 5x

Solving for variable 'x'.

Reorder the terms:
-13 + -7x + -5x + x2 = 13 + 5x + -13 + -5x

Combine like terms: -7x + -5x = -12x
-13 + -12x + x2 = 13 + 5x + -13 + -5x

Reorder the terms:
-13 + -12x + x2 = 13 + -13 + 5x + -5x

Combine like terms: 13 + -13 = 0
-13 + -12x + x2 = 0 + 5x + -5x
-13 + -12x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-13 + -12x + x2 = 0

Factor a trinomial.
(-1 + -1x)(13 + -1x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-1, 13}

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