x(5-x)=3(24-4x)

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Solution for x(5-x)=3(24-4x) equation: 


Simplifying
x(5 + -1x) = 3(24 + -4x)
(5 * x + -1x * x) = 3(24 + -4x)
(5x + -1x2) = 3(24 + -4x)
5x + -1x2 = (24 * 3 + -4x * 3)
5x + -1x2 = (72 + -12x)

Solving
5x + -1x2 = 72 + -12x

Solving for variable 'x'.

Reorder the terms:
-72 + 5x + 12x + -1x2 = 72 + -12x + -72 + 12x

Combine like terms: 5x + 12x = 17x
-72 + 17x + -1x2 = 72 + -12x + -72 + 12x

Reorder the terms:
-72 + 17x + -1x2 = 72 + -72 + -12x + 12x

Combine like terms: 72 + -72 = 0
-72 + 17x + -1x2 = 0 + -12x + 12x
-72 + 17x + -1x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
-72 + 17x + -1x2 = 0

Factor a trinomial.
(-9 + x)(8 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {9, 8}

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