(x-5)(40-x)=4(x-5)

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Solution for (x-5)(40-x)=4(x-5) equation: 


Simplifying
(x + -5)(40 + -1x) = 4(x + -5)

Reorder the terms:
(-5 + x)(40 + -1x) = 4(x + -5)

Multiply (-5 + x) * (40 + -1x)
(-5(40 + -1x) + x(40 + -1x)) = 4(x + -5)
((40 * -5 + -1x * -5) + x(40 + -1x)) = 4(x + -5)
((-200 + 5x) + x(40 + -1x)) = 4(x + -5)
(-200 + 5x + (40 * x + -1x * x)) = 4(x + -5)
(-200 + 5x + (40x + -1x2)) = 4(x + -5)

Combine like terms: 5x + 40x = 45x
(-200 + 45x + -1x2) = 4(x + -5)

Reorder the terms:
-200 + 45x + -1x2 = 4(-5 + x)
-200 + 45x + -1x2 = (-5 * 4 + x * 4)
-200 + 45x + -1x2 = (-20 + 4x)

Solving
-200 + 45x + -1x2 = -20 + 4x

Solving for variable 'x'.

Reorder the terms:
-200 + 20 + 45x + -4x + -1x2 = -20 + 4x + 20 + -4x

Combine like terms: -200 + 20 = -180
-180 + 45x + -4x + -1x2 = -20 + 4x + 20 + -4x

Combine like terms: 45x + -4x = 41x
-180 + 41x + -1x2 = -20 + 4x + 20 + -4x

Reorder the terms:
-180 + 41x + -1x2 = -20 + 20 + 4x + -4x

Combine like terms: -20 + 20 = 0
-180 + 41x + -1x2 = 0 + 4x + -4x
-180 + 41x + -1x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-180 + 41x + -1x2 = 0

Factor a trinomial.
(-36 + x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-36 + x)' equal to zero and attempt to solve:

Simplifying
-36 + x = 0

Solving
-36 + x = 0

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

Add '36' to each side of the equation.
-36 + 36 + x = 0 + 36

Combine like terms: -36 + 36 = 0
0 + x = 0 + 36
x = 0 + 36

Combine like terms: 0 + 36 = 36
x = 36

Simplifying
x = 36

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 = {36, 5}

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