(7x+42)(-2x+10)=0

Solution for (7x+42)(-2x+10)=0 equation:

Simplifying
(7x + 42)(-2x + 10) = 0

Reorder the terms:
(42 + 7x)(-2x + 10) = 0

Reorder the terms:
(42 + 7x)(10 + -2x) = 0

Multiply (42 + 7x) * (10 + -2x)
(42(10 + -2x) + 7x * (10 + -2x)) = 0
((10 * 42 + -2x * 42) + 7x * (10 + -2x)) = 0
((420 + -84x) + 7x * (10 + -2x)) = 0
(420 + -84x + (10 * 7x + -2x * 7x)) = 0
(420 + -84x + (70x + -14x2)) = 0

Combine like terms: -84x + 70x = -14x
(420 + -14x + -14x2) = 0

Solving
420 + -14x + -14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14'.
14(30 + -1x + -1x2) = 0

Factor a trinomial.
14((5 + -1x)(6 + x)) = 0

Ignore the factor 14.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {5, -6}