(42-7x)(2+4x)=0

Solution for (42-7x)(2+4x)=0 equation:

Simplifying
(42 + -7x)(2 + 4x) = 0

Multiply (42 + -7x) * (2 + 4x)
(42(2 + 4x) + -7x * (2 + 4x)) = 0
((2 * 42 + 4x * 42) + -7x * (2 + 4x)) = 0
((84 + 168x) + -7x * (2 + 4x)) = 0
(84 + 168x + (2 * -7x + 4x * -7x)) = 0
(84 + 168x + (-14x + -28x2)) = 0

Combine like terms: 168x + -14x = 154x
(84 + 154x + -28x2) = 0

Solving
84 + 154x + -28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14'.
14(6 + 11x + -2x2) = 0

Factor a trinomial.
14((6 + -1x)(1 + 2x)) = 0

Ignore the factor 14.
Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
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
Solution
x = {6, -0.5}