2x(x-5)=x+21

Solution for 2x(x-5)=x+21 equation:

Simplifying
2x(x + -5) = x + 21

Reorder the terms:
2x(-5 + x) = x + 21
(-5 * 2x + x * 2x) = x + 21
(-10x + 2x2) = x + 21

Reorder the terms:
-10x + 2x2 = 21 + x

Solving
-10x + 2x2 = 21 + x

Solving for variable 'x'.

Reorder the terms:
-21 + -10x + -1x + 2x2 = 21 + x + -21 + -1x

Combine like terms: -10x + -1x = -11x
-21 + -11x + 2x2 = 21 + x + -21 + -1x

Reorder the terms:
-21 + -11x + 2x2 = 21 + -21 + x + -1x

Combine like terms: 21 + -21 = 0
-21 + -11x + 2x2 = 0 + x + -1x
-21 + -11x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-21 + -11x + 2x2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.5, 7}