(5x-1)(6x-10)=0

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Solution for (5x-1)(6x-10)=0 equation: 


Simplifying
(5x + -1)(6x + -10) = 0

Reorder the terms:
(-1 + 5x)(6x + -10) = 0

Reorder the terms:
(-1 + 5x)(-10 + 6x) = 0

Multiply (-1 + 5x) * (-10 + 6x)
(-1(-10 + 6x) + 5x * (-10 + 6x)) = 0
((-10 * -1 + 6x * -1) + 5x * (-10 + 6x)) = 0
((10 + -6x) + 5x * (-10 + 6x)) = 0
(10 + -6x + (-10 * 5x + 6x * 5x)) = 0
(10 + -6x + (-50x + 30x2)) = 0

Combine like terms: -6x + -50x = -56x
(10 + -56x + 30x2) = 0

Solving
10 + -56x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -28x + 15x2) = 0

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

Ignore the factor 2.

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

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

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

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

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0.2, 1.666666667}

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