(2-x)(4-3x)=8x-19

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Solution for (2-x)(4-3x)=8x-19 equation: 


Simplifying
(2 + -1x)(4 + -3x) = 8x + -19

Multiply (2 + -1x) * (4 + -3x)
(2(4 + -3x) + -1x * (4 + -3x)) = 8x + -19
((4 * 2 + -3x * 2) + -1x * (4 + -3x)) = 8x + -19
((8 + -6x) + -1x * (4 + -3x)) = 8x + -19
(8 + -6x + (4 * -1x + -3x * -1x)) = 8x + -19
(8 + -6x + (-4x + 3x2)) = 8x + -19

Combine like terms: -6x + -4x = -10x
(8 + -10x + 3x2) = 8x + -19

Reorder the terms:
8 + -10x + 3x2 = -19 + 8x

Solving
8 + -10x + 3x2 = -19 + 8x

Solving for variable 'x'.

Reorder the terms:
8 + 19 + -10x + -8x + 3x2 = -19 + 8x + 19 + -8x

Combine like terms: 8 + 19 = 27
27 + -10x + -8x + 3x2 = -19 + 8x + 19 + -8x

Combine like terms: -10x + -8x = -18x
27 + -18x + 3x2 = -19 + 8x + 19 + -8x

Reorder the terms:
27 + -18x + 3x2 = -19 + 19 + 8x + -8x

Combine like terms: -19 + 19 = 0
27 + -18x + 3x2 = 0 + 8x + -8x
27 + -18x + 3x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
27 + -18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -6x + x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}

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