(5x-7)(13x-11)=0

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Solution for (5x-7)(13x-11)=0 equation: 


Simplifying
(5x + -7)(13x + -11) = 0

Reorder the terms:
(-7 + 5x)(13x + -11) = 0

Reorder the terms:
(-7 + 5x)(-11 + 13x) = 0

Multiply (-7 + 5x) * (-11 + 13x)
(-7(-11 + 13x) + 5x * (-11 + 13x)) = 0
((-11 * -7 + 13x * -7) + 5x * (-11 + 13x)) = 0
((77 + -91x) + 5x * (-11 + 13x)) = 0
(77 + -91x + (-11 * 5x + 13x * 5x)) = 0
(77 + -91x + (-55x + 65x2)) = 0

Combine like terms: -91x + -55x = -146x
(77 + -146x + 65x2) = 0

Solving
77 + -146x + 65x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(11 + -13x)(7 + -5x) = 0


Subproblem 1
Set the factor '(11 + -13x)' equal to zero and attempt to solve:

Simplifying
11 + -13x = 0

Solving
11 + -13x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -13x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -13x = 0 + -11
-13x = 0 + -11

Combine like terms: 0 + -11 = -11
-13x = -11

Divide each side by '-13'.
x = 0.8461538462

Simplifying
x = 0.8461538462

Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 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 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {0.8461538462, 1.4}

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