5(2x-3)(x-5)=0

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Solution for 5(2x-3)(x-5)=0 equation: 


Simplifying
5(2x + -3)(x + -5) = 0

Reorder the terms:
5(-3 + 2x)(x + -5) = 0

Reorder the terms:
5(-3 + 2x)(-5 + x) = 0

Multiply (-3 + 2x) * (-5 + x)
5(-3(-5 + x) + 2x * (-5 + x)) = 0
5((-5 * -3 + x * -3) + 2x * (-5 + x)) = 0
5((15 + -3x) + 2x * (-5 + x)) = 0
5(15 + -3x + (-5 * 2x + x * 2x)) = 0
5(15 + -3x + (-10x + 2x2)) = 0

Combine like terms: -3x + -10x = -13x
5(15 + -13x + 2x2) = 0
(15 * 5 + -13x * 5 + 2x2 * 5) = 0
(75 + -65x + 10x2) = 0

Solving
75 + -65x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(15 + -13x + 2x2) = 0

Factor a trinomial.
5((3 + -2x)(5 + -1x)) = 0

Ignore the factor 5.

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1.5, 5}

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