(3x+5)(7x-1)=0

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Solution for (3x+5)(7x-1)=0 equation: 


Simplifying
(3x + 5)(7x + -1) = 0

Reorder the terms:
(5 + 3x)(7x + -1) = 0

Reorder the terms:
(5 + 3x)(-1 + 7x) = 0

Multiply (5 + 3x) * (-1 + 7x)
(5(-1 + 7x) + 3x * (-1 + 7x)) = 0
((-1 * 5 + 7x * 5) + 3x * (-1 + 7x)) = 0
((-5 + 35x) + 3x * (-1 + 7x)) = 0
(-5 + 35x + (-1 * 3x + 7x * 3x)) = 0
(-5 + 35x + (-3x + 21x2)) = 0

Combine like terms: 35x + -3x = 32x
(-5 + 32x + 21x2) = 0

Solving
-5 + 32x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -3x)(1 + -7x) = 0


Subproblem 1
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

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

Simplifying
1 + -7x = 0

Solving
1 + -7x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Solution
x = {-1.666666667, 0.1428571429}

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