(5x-4)(2x-6)=0

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Solution for (5x-4)(2x-6)=0 equation: 


Simplifying
(5x + -4)(2x + -6) = 0

Reorder the terms:
(-4 + 5x)(2x + -6) = 0

Reorder the terms:
(-4 + 5x)(-6 + 2x) = 0

Multiply (-4 + 5x) * (-6 + 2x)
(-4(-6 + 2x) + 5x * (-6 + 2x)) = 0
((-6 * -4 + 2x * -4) + 5x * (-6 + 2x)) = 0
((24 + -8x) + 5x * (-6 + 2x)) = 0
(24 + -8x + (-6 * 5x + 2x * 5x)) = 0
(24 + -8x + (-30x + 10x2)) = 0

Combine like terms: -8x + -30x = -38x
(24 + -38x + 10x2) = 0

Solving
24 + -38x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -19x + 5x2) = 0

Factor a trinomial.
2((4 + -5x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 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 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8

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

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.8, 3}

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