(3x-9)(x-1)=7x-19

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Solution for (3x-9)(x-1)=7x-19 equation: 


Simplifying
(3x + -9)(x + -1) = 7x + -19

Reorder the terms:
(-9 + 3x)(x + -1) = 7x + -19

Reorder the terms:
(-9 + 3x)(-1 + x) = 7x + -19

Multiply (-9 + 3x) * (-1 + x)
(-9(-1 + x) + 3x * (-1 + x)) = 7x + -19
((-1 * -9 + x * -9) + 3x * (-1 + x)) = 7x + -19
((9 + -9x) + 3x * (-1 + x)) = 7x + -19
(9 + -9x + (-1 * 3x + x * 3x)) = 7x + -19
(9 + -9x + (-3x + 3x2)) = 7x + -19

Combine like terms: -9x + -3x = -12x
(9 + -12x + 3x2) = 7x + -19

Reorder the terms:
9 + -12x + 3x2 = -19 + 7x

Solving
9 + -12x + 3x2 = -19 + 7x

Solving for variable 'x'.

Reorder the terms:
9 + 19 + -12x + -7x + 3x2 = -19 + 7x + 19 + -7x

Combine like terms: 9 + 19 = 28
28 + -12x + -7x + 3x2 = -19 + 7x + 19 + -7x

Combine like terms: -12x + -7x = -19x
28 + -19x + 3x2 = -19 + 7x + 19 + -7x

Reorder the terms:
28 + -19x + 3x2 = -19 + 19 + 7x + -7x

Combine like terms: -19 + 19 = 0
28 + -19x + 3x2 = 0 + 7x + -7x
28 + -19x + 3x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
28 + -19x + 3x2 = 0

Factor a trinomial.
(7 + -3x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2.333333333, 4}

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