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

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


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

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

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

Multiply (-5 + 3x) * (2 + 7x)
(-5(2 + 7x) + 3x * (2 + 7x)) = 0
((2 * -5 + 7x * -5) + 3x * (2 + 7x)) = 0
((-10 + -35x) + 3x * (2 + 7x)) = 0
(-10 + -35x + (2 * 3x + 7x * 3x)) = 0
(-10 + -35x + (6x + 21x2)) = 0

Combine like terms: -35x + 6x = -29x
(-10 + -29x + 21x2) = 0

Solving
-10 + -29x + 21x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-2 + -7x)' equal to zero and attempt to solve:

Simplifying
-2 + -7x = 0

Solving
-2 + -7x = 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 + -7x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7x = 0 + 2
-7x = 0 + 2

Combine like terms: 0 + 2 = 2
-7x = 2

Divide each side by '-7'.
x = -0.2857142857

Simplifying
x = -0.2857142857

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-0.2857142857, 1.666666667}

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