0=-7(3x-7)(x+1)

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Solution for 0=-7(3x-7)(x+1) equation: 


Simplifying
0 = -7(3x + -7)(x + 1)

Reorder the terms:
0 = -7(-7 + 3x)(x + 1)

Reorder the terms:
0 = -7(-7 + 3x)(1 + x)

Multiply (-7 + 3x) * (1 + x)
0 = -7(-7(1 + x) + 3x * (1 + x))
0 = -7((1 * -7 + x * -7) + 3x * (1 + x))
0 = -7((-7 + -7x) + 3x * (1 + x))
0 = -7(-7 + -7x + (1 * 3x + x * 3x))
0 = -7(-7 + -7x + (3x + 3x2))

Combine like terms: -7x + 3x = -4x
0 = -7(-7 + -4x + 3x2)
0 = (-7 * -7 + -4x * -7 + 3x2 * -7)
0 = (49 + 28x + -21x2)

Solving
0 = 49 + 28x + -21x2

Solving for variable 'x'.

Combine like terms: 0 + -49 = -49
-49 + -28x + 21x2 = 49 + 28x + -21x2 + -49 + -28x + 21x2

Reorder the terms:
-49 + -28x + 21x2 = 49 + -49 + 28x + -28x + -21x2 + 21x2

Combine like terms: 49 + -49 = 0
-49 + -28x + 21x2 = 0 + 28x + -28x + -21x2 + 21x2
-49 + -28x + 21x2 = 28x + -28x + -21x2 + 21x2

Combine like terms: 28x + -28x = 0
-49 + -28x + 21x2 = 0 + -21x2 + 21x2
-49 + -28x + 21x2 = -21x2 + 21x2

Combine like terms: -21x2 + 21x2 = 0
-49 + -28x + 21x2 = 0

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

Factor a trinomial.
7((-1 + -1x)(7 + -3x)) = 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 '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-1, 2.333333333}

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