-3x(2x-7)=-3x+21-3x

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Solution for -3x(2x-7)=-3x+21-3x equation: 


Simplifying
-3x(2x + -7) = -3x + 21 + -3x

Reorder the terms:
-3x(-7 + 2x) = -3x + 21 + -3x
(-7 * -3x + 2x * -3x) = -3x + 21 + -3x
(21x + -6x2) = -3x + 21 + -3x

Reorder the terms:
21x + -6x2 = 21 + -3x + -3x

Combine like terms: -3x + -3x = -6x
21x + -6x2 = 21 + -6x

Solving
21x + -6x2 = 21 + -6x

Solving for variable 'x'.

Reorder the terms:
-21 + 21x + 6x + -6x2 = 21 + -6x + -21 + 6x

Combine like terms: 21x + 6x = 27x
-21 + 27x + -6x2 = 21 + -6x + -21 + 6x

Reorder the terms:
-21 + 27x + -6x2 = 21 + -21 + -6x + 6x

Combine like terms: 21 + -21 = 0
-21 + 27x + -6x2 = 0 + -6x + 6x
-21 + 27x + -6x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-21 + 27x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 9x + -2x2) = 0

Factor a trinomial.
3((-7 + 2x)(1 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5

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 = {3.5, 1}

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