684x+684(x+21)=19x(x+21)

Solution for 684x+684(x+21)=19x(x+21) equation:

Simplifying
684x + 684(x + 21) = 19x(x + 21)

Reorder the terms:
684x + 684(21 + x) = 19x(x + 21)
684x + (21 * 684 + x * 684) = 19x(x + 21)
684x + (14364 + 684x) = 19x(x + 21)

Reorder the terms:
14364 + 684x + 684x = 19x(x + 21)

Combine like terms: 684x + 684x = 1368x
14364 + 1368x = 19x(x + 21)

Reorder the terms:
14364 + 1368x = 19x(21 + x)
14364 + 1368x = (21 * 19x + x * 19x)
14364 + 1368x = (399x + 19x2)

Solving
14364 + 1368x = 399x + 19x2

Solving for variable 'x'.

Combine like terms: 1368x + -399x = 969x
14364 + 969x + -19x2 = 399x + 19x2 + -399x + -19x2

Reorder the terms:
14364 + 969x + -19x2 = 399x + -399x + 19x2 + -19x2

Combine like terms: 399x + -399x = 0
14364 + 969x + -19x2 = 0 + 19x2 + -19x2
14364 + 969x + -19x2 = 19x2 + -19x2

Combine like terms: 19x2 + -19x2 = 0
14364 + 969x + -19x2 = 0

Factor out the Greatest Common Factor (GCF), '19'.
19(756 + 51x + -1x2) = 0

Factor a trinomial.
19((63 + -1x)(12 + x)) = 0

Ignore the factor 19.
Subproblem 1
Set the factor '(63 + -1x)' equal to zero and attempt to solve:

Simplifying
63 + -1x = 0

Solving
63 + -1x = 0

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

Add '-63' to each side of the equation.
63 + -63 + -1x = 0 + -63

Combine like terms: 63 + -63 = 0
0 + -1x = 0 + -63
-1x = 0 + -63

Combine like terms: 0 + -63 = -63
-1x = -63

Divide each side by '-1'.
x = 63

Simplifying
x = 63
Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {63, -12}