4(5-X)-3(-X-5)(X-5)=0

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Solution for 4(5-X)-3(-X-5)(X-5)=0 equation: 


Simplifying
4(5 + -1X) + -3(-1X + -5)(X + -5) = 0
(5 * 4 + -1X * 4) + -3(-1X + -5)(X + -5) = 0
(20 + -4X) + -3(-1X + -5)(X + -5) = 0

Reorder the terms:
20 + -4X + -3(-5 + -1X)(X + -5) = 0

Reorder the terms:
20 + -4X + -3(-5 + -1X)(-5 + X) = 0

Multiply (-5 + -1X) * (-5 + X)
20 + -4X + -3(-5(-5 + X) + -1X * (-5 + X)) = 0
20 + -4X + -3((-5 * -5 + X * -5) + -1X * (-5 + X)) = 0
20 + -4X + -3((25 + -5X) + -1X * (-5 + X)) = 0
20 + -4X + -3(25 + -5X + (-5 * -1X + X * -1X)) = 0
20 + -4X + -3(25 + -5X + (5X + -1X2)) = 0

Combine like terms: -5X + 5X = 0
20 + -4X + -3(25 + 0 + -1X2) = 0
20 + -4X + -3(25 + -1X2) = 0
20 + -4X + (25 * -3 + -1X2 * -3) = 0
20 + -4X + (-75 + 3X2) = 0

Reorder the terms:
20 + -75 + -4X + 3X2 = 0

Combine like terms: 20 + -75 = -55
-55 + -4X + 3X2 = 0

Solving
-55 + -4X + 3X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-11 + -3X)(5 + -1X) = 0


Subproblem 1
Set the factor '(-11 + -3X)' equal to zero and attempt to solve:

Simplifying
-11 + -3X = 0

Solving
-11 + -3X = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3X = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3X = 0 + 11
-3X = 0 + 11

Combine like terms: 0 + 11 = 11
-3X = 11

Divide each side by '-3'.
X = -3.666666667

Simplifying
X = -3.666666667

Subproblem 2
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
Solution
X = {-3.666666667, 5}

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