(-5x+2)(7x-13)=0

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Solution for (-5x+2)(7x-13)=0 equation: 


Simplifying
(-5x + 2)(7x + -13) = 0

Reorder the terms:
(2 + -5x)(7x + -13) = 0

Reorder the terms:
(2 + -5x)(-13 + 7x) = 0

Multiply (2 + -5x) * (-13 + 7x)
(2(-13 + 7x) + -5x * (-13 + 7x)) = 0
((-13 * 2 + 7x * 2) + -5x * (-13 + 7x)) = 0
((-26 + 14x) + -5x * (-13 + 7x)) = 0
(-26 + 14x + (-13 * -5x + 7x * -5x)) = 0
(-26 + 14x + (65x + -35x2)) = 0

Combine like terms: 14x + 65x = 79x
(-26 + 79x + -35x2) = 0

Solving
-26 + 79x + -35x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-13 + 7x)(2 + -5x) = 0


Subproblem 1
Set the factor '(-13 + 7x)' equal to zero and attempt to solve:

Simplifying
-13 + 7x = 0

Solving
-13 + 7x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 7x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 7x = 0 + 13
7x = 0 + 13

Combine like terms: 0 + 13 = 13
7x = 13

Divide each side by '7'.
x = 1.857142857

Simplifying
x = 1.857142857

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

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {1.857142857, 0.4}

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