(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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