3x(x-1)-7(x-2)=7

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Solution for 3x(x-1)-7(x-2)=7 equation: 


Simplifying
3x(x + -1) + -7(x + -2) = 7

Reorder the terms:
3x(-1 + x) + -7(x + -2) = 7
(-1 * 3x + x * 3x) + -7(x + -2) = 7
(-3x + 3x2) + -7(x + -2) = 7

Reorder the terms:
-3x + 3x2 + -7(-2 + x) = 7
-3x + 3x2 + (-2 * -7 + x * -7) = 7
-3x + 3x2 + (14 + -7x) = 7

Reorder the terms:
14 + -3x + -7x + 3x2 = 7

Combine like terms: -3x + -7x = -10x
14 + -10x + 3x2 = 7

Solving
14 + -10x + 3x2 = 7

Solving for variable 'x'.

Reorder the terms:
14 + -7 + -10x + 3x2 = 7 + -7

Combine like terms: 14 + -7 = 7
7 + -10x + 3x2 = 7 + -7

Combine like terms: 7 + -7 = 0
7 + -10x + 3x2 = 0

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


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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