7x(x-9)(2x-5)=0

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Solution for 7x(x-9)(2x-5)=0 equation: 


Simplifying
7x(x + -9)(2x + -5) = 0

Reorder the terms:
7x(-9 + x)(2x + -5) = 0

Reorder the terms:
7x(-9 + x)(-5 + 2x) = 0

Multiply (-9 + x) * (-5 + 2x)
7x(-9(-5 + 2x) + x(-5 + 2x)) = 0
7x((-5 * -9 + 2x * -9) + x(-5 + 2x)) = 0
7x((45 + -18x) + x(-5 + 2x)) = 0
7x(45 + -18x + (-5 * x + 2x * x)) = 0
7x(45 + -18x + (-5x + 2x2)) = 0

Combine like terms: -18x + -5x = -23x
7x(45 + -23x + 2x2) = 0
(45 * 7x + -23x * 7x + 2x2 * 7x) = 0
(315x + -161x2 + 14x3) = 0

Solving
315x + -161x2 + 14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x'.
7x(45 + -23x + 2x2) = 0

Factor a trinomial.
7x((5 + -2x)(9 + -1x)) = 0

Ignore the factor 7.

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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 3
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, 2.5, 9}

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