(4x+2)(7x-3)=0

Solution for (4x+2)(7x-3)=0 equation:

Simplifying
(4x + 2)(7x + -3) = 0

Reorder the terms:
(2 + 4x)(7x + -3) = 0

Reorder the terms:
(2 + 4x)(-3 + 7x) = 0

Multiply (2 + 4x) * (-3 + 7x)
(2(-3 + 7x) + 4x * (-3 + 7x)) = 0
((-3 * 2 + 7x * 2) + 4x * (-3 + 7x)) = 0
((-6 + 14x) + 4x * (-3 + 7x)) = 0
(-6 + 14x + (-3 * 4x + 7x * 4x)) = 0
(-6 + 14x + (-12x + 28x2)) = 0

Combine like terms: 14x + -12x = 2x
(-6 + 2x + 28x2) = 0

Solving
-6 + 2x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + x + 14x2) = 0

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

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

Simplifying
-1 + -2x = 0

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

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-0.5, 0.4285714286}