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

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

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

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

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

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

Combine like terms: 2x + -7x = -5x
3(-2 + -5x + 7x2) = 0
(-2 * 3 + -5x * 3 + 7x2 * 3) = 0
(-6 + -15x + 21x2) = 0

Solving
-6 + -15x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -5x + 7x2) = 0

Factor a trinomial.
3((-2 + -7x)(1 + -1x)) = 0

Ignore the factor 3.
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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-0.2857142857, 1}