42=21x^2+21x

Solution for 42=21x^2+21x equation:

Simplifying
42 = 21x2 + 21x

Reorder the terms:
42 = 21x + 21x2

Solving
42 = 21x + 21x2

Solving for variable 'x'.

Reorder the terms:
42 + -21x + -21x2 = 21x + -21x + 21x2 + -21x2

Combine like terms: 21x + -21x = 0
42 + -21x + -21x2 = 0 + 21x2 + -21x2
42 + -21x + -21x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
42 + -21x + -21x2 = 0

Factor out the Greatest Common Factor (GCF), '21'.
21(2 + -1x + -1x2) = 0

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

Ignore the factor 21.
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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {1, -2}