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

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


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

Reorder the terms:
3x(-7 + x) + 7(x + -7) = 0
(-7 * 3x + x * 3x) + 7(x + -7) = 0
(-21x + 3x2) + 7(x + -7) = 0

Reorder the terms:
-21x + 3x2 + 7(-7 + x) = 0
-21x + 3x2 + (-7 * 7 + x * 7) = 0
-21x + 3x2 + (-49 + 7x) = 0

Reorder the terms:
-49 + -21x + 7x + 3x2 = 0

Combine like terms: -21x + 7x = -14x
-49 + -14x + 3x2 = 0

Solving
-49 + -14x + 3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2.333333333, 7}

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