(45-2x)(30-2x)*x=0

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Solution for (45-2x)(30-2x)*x=0 equation: 


Simplifying
(45 + -2x)(30 + -2x) * x = 0

Reorder the terms for easier multiplication:
x(45 + -2x)(30 + -2x) = 0

Multiply (45 + -2x) * (30 + -2x)
x(45(30 + -2x) + -2x * (30 + -2x)) = 0
x((30 * 45 + -2x * 45) + -2x * (30 + -2x)) = 0
x((1350 + -90x) + -2x * (30 + -2x)) = 0
x(1350 + -90x + (30 * -2x + -2x * -2x)) = 0
x(1350 + -90x + (-60x + 4x2)) = 0

Combine like terms: -90x + -60x = -150x
x(1350 + -150x + 4x2) = 0
(1350 * x + -150x * x + 4x2 * x) = 0
(1350x + -150x2 + 4x3) = 0

Solving
1350x + -150x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(675 + -75x + 2x2) = 0

Factor a trinomial.
2x((15 + -1x)(45 + -2x)) = 0

Ignore the factor 2.

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 '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15

Subproblem 3
Set the factor '(45 + -2x)' equal to zero and attempt to solve:

Simplifying
45 + -2x = 0

Solving
45 + -2x = 0

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

Add '-45' to each side of the equation.
45 + -45 + -2x = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -2x = 0 + -45
-2x = 0 + -45

Combine like terms: 0 + -45 = -45
-2x = -45

Divide each side by '-2'.
x = 22.5

Simplifying
x = 22.5
Solution
x = {0, 15, 22.5}

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