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

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

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

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

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

Multiply (-3 + 2x) * (2 + 7x)
(-3(2 + 7x) + 2x * (2 + 7x)) = 0
((2 * -3 + 7x * -3) + 2x * (2 + 7x)) = 0
((-6 + -21x) + 2x * (2 + 7x)) = 0
(-6 + -21x + (2 * 2x + 7x * 2x)) = 0
(-6 + -21x + (4x + 14x2)) = 0

Combine like terms: -21x + 4x = -17x
(-6 + -17x + 14x2) = 0

Solving
-6 + -17x + 14x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -7x)(3 + -2x) = 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 '(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 = {-0.2857142857, 1.5}