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

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


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

Reorder the terms:
3x(-1 + x) + 7(x + -1) = 0
(-1 * 3x + x * 3x) + 7(x + -1) = 0
(-3x + 3x2) + 7(x + -1) = 0

Reorder the terms:
-3x + 3x2 + 7(-1 + x) = 0
-3x + 3x2 + (-1 * 7 + x * 7) = 0
-3x + 3x2 + (-7 + 7x) = 0

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

Combine like terms: -3x + 7x = 4x
-7 + 4x + 3x2 = 0

Solving
-7 + 4x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -3x)(1 + -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 '(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 = {-2.333333333, 1}

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