10(x-4)(2x-9)=0

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Solution for 10(x-4)(2x-9)=0 equation: 


Simplifying
10(x + -4)(2x + -9) = 0

Reorder the terms:
10(-4 + x)(2x + -9) = 0

Reorder the terms:
10(-4 + x)(-9 + 2x) = 0

Multiply (-4 + x) * (-9 + 2x)
10(-4(-9 + 2x) + x(-9 + 2x)) = 0
10((-9 * -4 + 2x * -4) + x(-9 + 2x)) = 0
10((36 + -8x) + x(-9 + 2x)) = 0
10(36 + -8x + (-9 * x + 2x * x)) = 0
10(36 + -8x + (-9x + 2x2)) = 0

Combine like terms: -8x + -9x = -17x
10(36 + -17x + 2x2) = 0
(36 * 10 + -17x * 10 + 2x2 * 10) = 0
(360 + -170x + 20x2) = 0

Solving
360 + -170x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(36 + -17x + 2x2) = 0

Factor a trinomial.
10((4 + -1x)(9 + -2x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {4, 4.5}

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