(5x-2)(3x-7)=0

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Solution for (5x-2)(3x-7)=0 equation: 


Simplifying
(5x + -2)(3x + -7) = 0

Reorder the terms:
(-2 + 5x)(3x + -7) = 0

Reorder the terms:
(-2 + 5x)(-7 + 3x) = 0

Multiply (-2 + 5x) * (-7 + 3x)
(-2(-7 + 3x) + 5x * (-7 + 3x)) = 0
((-7 * -2 + 3x * -2) + 5x * (-7 + 3x)) = 0
((14 + -6x) + 5x * (-7 + 3x)) = 0
(14 + -6x + (-7 * 5x + 3x * 5x)) = 0
(14 + -6x + (-35x + 15x2)) = 0

Combine like terms: -6x + -35x = -41x
(14 + -41x + 15x2) = 0

Solving
14 + -41x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -5x)(7 + -3x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0.4, 2.333333333}

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