(7x-10)(13x-4)=0

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Solution for (7x-10)(13x-4)=0 equation: 


Simplifying
(7x + -10)(13x + -4) = 0

Reorder the terms:
(-10 + 7x)(13x + -4) = 0

Reorder the terms:
(-10 + 7x)(-4 + 13x) = 0

Multiply (-10 + 7x) * (-4 + 13x)
(-10(-4 + 13x) + 7x * (-4 + 13x)) = 0
((-4 * -10 + 13x * -10) + 7x * (-4 + 13x)) = 0
((40 + -130x) + 7x * (-4 + 13x)) = 0
(40 + -130x + (-4 * 7x + 13x * 7x)) = 0
(40 + -130x + (-28x + 91x2)) = 0

Combine like terms: -130x + -28x = -158x
(40 + -158x + 91x2) = 0

Solving
40 + -158x + 91x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -13x)(10 + -7x) = 0


Subproblem 1
Set the factor '(4 + -13x)' equal to zero and attempt to solve:

Simplifying
4 + -13x = 0

Solving
4 + -13x = 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 + -13x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -13x = 0 + -4
-13x = 0 + -4

Combine like terms: 0 + -4 = -4
-13x = -4

Divide each side by '-13'.
x = 0.3076923077

Simplifying
x = 0.3076923077

Subproblem 2
Set the factor '(10 + -7x)' equal to zero and attempt to solve:

Simplifying
10 + -7x = 0

Solving
10 + -7x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -7x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -7x = 0 + -10
-7x = 0 + -10

Combine like terms: 0 + -10 = -10
-7x = -10

Divide each side by '-7'.
x = 1.428571429

Simplifying
x = 1.428571429
Solution
x = {0.3076923077, 1.428571429}

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