3x-21+4x=-7x(-x+3)

Solution for 3x-21+4x=-7x(-x+3) equation:

Simplifying
3x + -21 + 4x = -7x(-1x + 3)

Reorder the terms:
-21 + 3x + 4x = -7x(-1x + 3)

Combine like terms: 3x + 4x = 7x
-21 + 7x = -7x(-1x + 3)

Reorder the terms:
-21 + 7x = -7x(3 + -1x)
-21 + 7x = (3 * -7x + -1x * -7x)
-21 + 7x = (-21x + 7x2)

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

Solving for variable 'x'.

Combine like terms: 7x + 21x = 28x
-21 + 28x + -7x2 = -21x + 7x2 + 21x + -7x2

Reorder the terms:
-21 + 28x + -7x2 = -21x + 21x + 7x2 + -7x2

Combine like terms: -21x + 21x = 0
-21 + 28x + -7x2 = 0 + 7x2 + -7x2
-21 + 28x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-21 + 28x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + 4x + -1x2) = 0

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

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
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
Solution
x = {3, 1}