6(2x-5)(x-5)=0

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Solution for 6(2x-5)(x-5)=0 equation: 


Simplifying
6(2x + -5)(x + -5) = 0

Reorder the terms:
6(-5 + 2x)(x + -5) = 0

Reorder the terms:
6(-5 + 2x)(-5 + x) = 0

Multiply (-5 + 2x) * (-5 + x)
6(-5(-5 + x) + 2x * (-5 + x)) = 0
6((-5 * -5 + x * -5) + 2x * (-5 + x)) = 0
6((25 + -5x) + 2x * (-5 + x)) = 0
6(25 + -5x + (-5 * 2x + x * 2x)) = 0
6(25 + -5x + (-10x + 2x2)) = 0

Combine like terms: -5x + -10x = -15x
6(25 + -15x + 2x2) = 0
(25 * 6 + -15x * 6 + 2x2 * 6) = 0
(150 + -90x + 12x2) = 0

Solving
150 + -90x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(25 + -15x + 2x2) = 0

Factor a trinomial.
6((5 + -2x)(5 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
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 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 = {2.5, 5}

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