100x(x-30)=50x(80-x)

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Solution for 100x(x-30)=50x(80-x) equation:


Simplifying
100x(x + -30) = 50x(80 + -1x)

Reorder the terms:
100x(-30 + x) = 50x(80 + -1x)
(-30 * 100x + x * 100x) = 50x(80 + -1x)
(-3000x + 100x2) = 50x(80 + -1x)
-3000x + 100x2 = (80 * 50x + -1x * 50x)
-3000x + 100x2 = (4000x + -50x2)

Solving
-3000x + 100x2 = 4000x + -50x2

Solving for variable 'x'.

Reorder the terms:
-3000x + -4000x + 100x2 + 50x2 = 4000x + -50x2 + -4000x + 50x2

Combine like terms: -3000x + -4000x = -7000x
-7000x + 100x2 + 50x2 = 4000x + -50x2 + -4000x + 50x2

Combine like terms: 100x2 + 50x2 = 150x2
-7000x + 150x2 = 4000x + -50x2 + -4000x + 50x2

Reorder the terms:
-7000x + 150x2 = 4000x + -4000x + -50x2 + 50x2

Combine like terms: 4000x + -4000x = 0
-7000x + 150x2 = 0 + -50x2 + 50x2
-7000x + 150x2 = -50x2 + 50x2

Combine like terms: -50x2 + 50x2 = 0
-7000x + 150x2 = 0

Factor out the Greatest Common Factor (GCF), '50x'.
50x(-140 + 3x) = 0

Ignore the factor 50.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-140 + 3x)' equal to zero and attempt to solve:

Simplifying
-140 + 3x = 0

Solving
-140 + 3x = 0

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

Add '140' to each side of the equation.
-140 + 140 + 3x = 0 + 140

Combine like terms: -140 + 140 = 0
0 + 3x = 0 + 140
3x = 0 + 140

Combine like terms: 0 + 140 = 140
3x = 140

Divide each side by '3'.
x = 46.66666667

Simplifying
x = 46.66666667
Solution
x = {0, 46.66666667}

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