(2x-21)(x+4)=0

Solution for (2x-21)(x+4)=0 equation:

Simplifying
(2x + -21)(x + 4) = 0

Reorder the terms:
(-21 + 2x)(x + 4) = 0

Reorder the terms:
(-21 + 2x)(4 + x) = 0

Multiply (-21 + 2x) * (4 + x)
(-21(4 + x) + 2x * (4 + x)) = 0
((4 * -21 + x * -21) + 2x * (4 + x)) = 0
((-84 + -21x) + 2x * (4 + x)) = 0
(-84 + -21x + (4 * 2x + x * 2x)) = 0
(-84 + -21x + (8x + 2x2)) = 0

Combine like terms: -21x + 8x = -13x
(-84 + -13x + 2x2) = 0

Solving
-84 + -13x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x)(21 + -2x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(21 + -2x)' equal to zero and attempt to solve:

Simplifying
21 + -2x = 0

Solving
21 + -2x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -2x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -2x = 0 + -21
-2x = 0 + -21

Combine like terms: 0 + -21 = -21
-2x = -21

Divide each side by '-2'.
x = 10.5

Simplifying
x = 10.5
Solution
x = {-4, 10.5}