(200+3x)(x-60)=200x

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Solution for (200+3x)(x-60)=200x equation: 


Simplifying
(200 + 3x)(x + -60) = 200x

Reorder the terms:
(200 + 3x)(-60 + x) = 200x

Multiply (200 + 3x) * (-60 + x)
(200(-60 + x) + 3x * (-60 + x)) = 200x
((-60 * 200 + x * 200) + 3x * (-60 + x)) = 200x
((-12000 + 200x) + 3x * (-60 + x)) = 200x
(-12000 + 200x + (-60 * 3x + x * 3x)) = 200x
(-12000 + 200x + (-180x + 3x2)) = 200x

Combine like terms: 200x + -180x = 20x
(-12000 + 20x + 3x2) = 200x

Solving
-12000 + 20x + 3x2 = 200x

Solving for variable 'x'.

Reorder the terms:
-12000 + 20x + -200x + 3x2 = 200x + -200x

Combine like terms: 20x + -200x = -180x
-12000 + -180x + 3x2 = 200x + -200x

Combine like terms: 200x + -200x = 0
-12000 + -180x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4000 + -60x + x2) = 0

Factor a trinomial.
3((-40 + -1x)(100 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-40 + -1x)' equal to zero and attempt to solve:

Simplifying
-40 + -1x = 0

Solving
-40 + -1x = 0

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

Add '40' to each side of the equation.
-40 + 40 + -1x = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -1x = 0 + 40
-1x = 0 + 40

Combine like terms: 0 + 40 = 40
-1x = 40

Divide each side by '-1'.
x = -40

Simplifying
x = -40

Subproblem 2
Set the factor '(100 + -1x)' equal to zero and attempt to solve:

Simplifying
100 + -1x = 0

Solving
100 + -1x = 0

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

Add '-100' to each side of the equation.
100 + -100 + -1x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1x = 0 + -100
-1x = 0 + -100

Combine like terms: 0 + -100 = -100
-1x = -100

Divide each side by '-1'.
x = 100

Simplifying
x = 100
Solution
x = {-40, 100}

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