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

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


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

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

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

Multiply (-5 + 5x) * (-2 + 6x)
(-5(-2 + 6x) + 5x * (-2 + 6x)) = 0
((-2 * -5 + 6x * -5) + 5x * (-2 + 6x)) = 0
((10 + -30x) + 5x * (-2 + 6x)) = 0
(10 + -30x + (-2 * 5x + 6x * 5x)) = 0
(10 + -30x + (-10x + 30x2)) = 0

Combine like terms: -30x + -10x = -40x
(10 + -40x + 30x2) = 0

Solving
10 + -40x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + -4x + 3x2) = 0

Factor a trinomial.
10((1 + -3x)(1 + -1x)) = 0

Ignore the factor 10.

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0.3333333333, 1}

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