(x-30)(100-2x)=200

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Solution for (x-30)(100-2x)=200 equation: 


Simplifying
(x + -30)(100 + -2x) = 200

Reorder the terms:
(-30 + x)(100 + -2x) = 200

Multiply (-30 + x) * (100 + -2x)
(-30(100 + -2x) + x(100 + -2x)) = 200
((100 * -30 + -2x * -30) + x(100 + -2x)) = 200
((-3000 + 60x) + x(100 + -2x)) = 200
(-3000 + 60x + (100 * x + -2x * x)) = 200
(-3000 + 60x + (100x + -2x2)) = 200

Combine like terms: 60x + 100x = 160x
(-3000 + 160x + -2x2) = 200

Solving
-3000 + 160x + -2x2 = 200

Solving for variable 'x'.

Reorder the terms:
-3000 + -200 + 160x + -2x2 = 200 + -200

Combine like terms: -3000 + -200 = -3200
-3200 + 160x + -2x2 = 200 + -200

Combine like terms: 200 + -200 = 0
-3200 + 160x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1600 + 80x + -1x2) = 0

Factor a trinomial.
2((-40 + x)(40 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-40 + x = 0

Solving
-40 + x = 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 + x = 0 + 40

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

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

Simplifying
x = 40

Subproblem 2
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
Solution
x = {40, 40}

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