8x-7x(x+3)=x-21

Solution for 8x-7x(x+3)=x-21 equation:

Simplifying
8x + -7x(x + 3) = x + -21

Reorder the terms:
8x + -7x(3 + x) = x + -21
8x + (3 * -7x + x * -7x) = x + -21
8x + (-21x + -7x2) = x + -21

Combine like terms: 8x + -21x = -13x
-13x + -7x2 = x + -21

Reorder the terms:
-13x + -7x2 = -21 + x

Solving
-13x + -7x2 = -21 + x

Solving for variable 'x'.

Reorder the terms:
21 + -13x + -1x + -7x2 = -21 + x + 21 + -1x

Combine like terms: -13x + -1x = -14x
21 + -14x + -7x2 = -21 + x + 21 + -1x

Reorder the terms:
21 + -14x + -7x2 = -21 + 21 + x + -1x

Combine like terms: -21 + 21 = 0
21 + -14x + -7x2 = 0 + x + -1x
21 + -14x + -7x2 = x + -1x

Combine like terms: x + -1x = 0
21 + -14x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + -2x + -1x2) = 0

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {1, -3}