(7x+2)(3x-1)=0

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Solution for (7x+2)(3x-1)=0 equation: 


Simplifying
(7x + 2)(3x + -1) = 0

Reorder the terms:
(2 + 7x)(3x + -1) = 0

Reorder the terms:
(2 + 7x)(-1 + 3x) = 0

Multiply (2 + 7x) * (-1 + 3x)
(2(-1 + 3x) + 7x * (-1 + 3x)) = 0
((-1 * 2 + 3x * 2) + 7x * (-1 + 3x)) = 0
((-2 + 6x) + 7x * (-1 + 3x)) = 0
(-2 + 6x + (-1 * 7x + 3x * 7x)) = 0
(-2 + 6x + (-7x + 21x2)) = 0

Combine like terms: 6x + -7x = -1x
(-2 + -1x + 21x2) = 0

Solving
-2 + -1x + 21x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -7x)(1 + -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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-0.2857142857, 0.3333333333}

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