(2x+1)(x-3)=x^2+21

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Solution for (2x+1)(x-3)=x^2+21 equation: 


Simplifying
(2x + 1)(x + -3) = x2 + 21

Reorder the terms:
(1 + 2x)(x + -3) = x2 + 21

Reorder the terms:
(1 + 2x)(-3 + x) = x2 + 21

Multiply (1 + 2x) * (-3 + x)
(1(-3 + x) + 2x * (-3 + x)) = x2 + 21
((-3 * 1 + x * 1) + 2x * (-3 + x)) = x2 + 21
((-3 + 1x) + 2x * (-3 + x)) = x2 + 21
(-3 + 1x + (-3 * 2x + x * 2x)) = x2 + 21
(-3 + 1x + (-6x + 2x2)) = x2 + 21

Combine like terms: 1x + -6x = -5x
(-3 + -5x + 2x2) = x2 + 21

Reorder the terms:
-3 + -5x + 2x2 = 21 + x2

Solving
-3 + -5x + 2x2 = 21 + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -21 + -5x + 2x2 + -1x2 = 21 + x2 + -21 + -1x2

Combine like terms: -3 + -21 = -24
-24 + -5x + 2x2 + -1x2 = 21 + x2 + -21 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-24 + -5x + 1x2 = 21 + x2 + -21 + -1x2

Reorder the terms:
-24 + -5x + 1x2 = 21 + -21 + x2 + -1x2

Combine like terms: 21 + -21 = 0
-24 + -5x + 1x2 = 0 + x2 + -1x2
-24 + -5x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-24 + -5x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3, 8}

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