(4x-5)(13x-5)=25

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Solution for (4x-5)(13x-5)=25 equation: 


Simplifying
(4x + -5)(13x + -5) = 25

Reorder the terms:
(-5 + 4x)(13x + -5) = 25

Reorder the terms:
(-5 + 4x)(-5 + 13x) = 25

Multiply (-5 + 4x) * (-5 + 13x)
(-5(-5 + 13x) + 4x * (-5 + 13x)) = 25
((-5 * -5 + 13x * -5) + 4x * (-5 + 13x)) = 25
((25 + -65x) + 4x * (-5 + 13x)) = 25
(25 + -65x + (-5 * 4x + 13x * 4x)) = 25
(25 + -65x + (-20x + 52x2)) = 25

Combine like terms: -65x + -20x = -85x
(25 + -85x + 52x2) = 25

Add '-25' to each side of the equation.
25 + -85x + -25 + 52x2 = 25 + -25

Reorder the terms:
25 + -25 + -85x + 52x2 = 25 + -25

Combine like terms: 25 + -25 = 0
0 + -85x + 52x2 = 25 + -25
-85x + 52x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-85x + 52x2 = 0

Solving
-85x + 52x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-85 + 52x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-85 + 52x)' equal to zero and attempt to solve:

Simplifying
-85 + 52x = 0

Solving
-85 + 52x = 0

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

Add '85' to each side of the equation.
-85 + 85 + 52x = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 52x = 0 + 85
52x = 0 + 85

Combine like terms: 0 + 85 = 85
52x = 85

Divide each side by '52'.
x = 1.634615385

Simplifying
x = 1.634615385
Solution
x = {0, 1.634615385}

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