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

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

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

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

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

Multiply (1 + 7x) * (-3 + 2x)
(1(-3 + 2x) + 7x * (-3 + 2x)) = 0
((-3 * 1 + 2x * 1) + 7x * (-3 + 2x)) = 0
((-3 + 2x) + 7x * (-3 + 2x)) = 0
(-3 + 2x + (-3 * 7x + 2x * 7x)) = 0
(-3 + 2x + (-21x + 14x2)) = 0

Combine like terms: 2x + -21x = -19x
(-3 + -19x + 14x2) = 0

Solving
-3 + -19x + 14x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.1428571429, 1.5}