x(5-x)=7(x-9)

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Solution for x(5-x)=7(x-9) equation: 


Simplifying
x(5 + -1x) = 7(x + -9)
(5 * x + -1x * x) = 7(x + -9)
(5x + -1x2) = 7(x + -9)

Reorder the terms:
5x + -1x2 = 7(-9 + x)
5x + -1x2 = (-9 * 7 + x * 7)
5x + -1x2 = (-63 + 7x)

Solving
5x + -1x2 = -63 + 7x

Solving for variable 'x'.

Reorder the terms:
63 + 5x + -7x + -1x2 = -63 + 7x + 63 + -7x

Combine like terms: 5x + -7x = -2x
63 + -2x + -1x2 = -63 + 7x + 63 + -7x

Reorder the terms:
63 + -2x + -1x2 = -63 + 63 + 7x + -7x

Combine like terms: -63 + 63 = 0
63 + -2x + -1x2 = 0 + 7x + -7x
63 + -2x + -1x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
63 + -2x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(9 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {7, -9}

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