(2x-7)(4x-10)=0

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Solution for (2x-7)(4x-10)=0 equation: 


Simplifying
(2x + -7)(4x + -10) = 0

Reorder the terms:
(-7 + 2x)(4x + -10) = 0

Reorder the terms:
(-7 + 2x)(-10 + 4x) = 0

Multiply (-7 + 2x) * (-10 + 4x)
(-7(-10 + 4x) + 2x * (-10 + 4x)) = 0
((-10 * -7 + 4x * -7) + 2x * (-10 + 4x)) = 0
((70 + -28x) + 2x * (-10 + 4x)) = 0
(70 + -28x + (-10 * 2x + 4x * 2x)) = 0
(70 + -28x + (-20x + 8x2)) = 0

Combine like terms: -28x + -20x = -48x
(70 + -48x + 8x2) = 0

Solving
70 + -48x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + -24x + 4x2) = 0

Factor a trinomial.
2((5 + -2x)(7 + -2x)) = 0

Ignore the factor 2.

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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {2.5, 3.5}

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