(4x-50)(90-30x)=0

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Solution for (4x-50)(90-30x)=0 equation: 


Simplifying
(4x + -50)(90 + -30x) = 0

Reorder the terms:
(-50 + 4x)(90 + -30x) = 0

Multiply (-50 + 4x) * (90 + -30x)
(-50(90 + -30x) + 4x * (90 + -30x)) = 0
((90 * -50 + -30x * -50) + 4x * (90 + -30x)) = 0
((-4500 + 1500x) + 4x * (90 + -30x)) = 0
(-4500 + 1500x + (90 * 4x + -30x * 4x)) = 0
(-4500 + 1500x + (360x + -120x2)) = 0

Combine like terms: 1500x + 360x = 1860x
(-4500 + 1860x + -120x2) = 0

Solving
-4500 + 1860x + -120x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '60'.
60(-75 + 31x + -2x2) = 0

Factor a trinomial.
60((-25 + 2x)(3 + -1x)) = 0

Ignore the factor 60.

Subproblem 1
Set the factor '(-25 + 2x)' equal to zero and attempt to solve:

Simplifying
-25 + 2x = 0

Solving
-25 + 2x = 0

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

Add '25' to each side of the equation.
-25 + 25 + 2x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 2x = 0 + 25
2x = 0 + 25

Combine like terms: 0 + 25 = 25
2x = 25

Divide each side by '2'.
x = 12.5

Simplifying
x = 12.5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {12.5, 3}

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