(3x-4)(x-6)=17

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Solution for (3x-4)(x-6)=17 equation: 


Simplifying
(3x + -4)(x + -6) = 17

Reorder the terms:
(-4 + 3x)(x + -6) = 17

Reorder the terms:
(-4 + 3x)(-6 + x) = 17

Multiply (-4 + 3x) * (-6 + x)
(-4(-6 + x) + 3x * (-6 + x)) = 17
((-6 * -4 + x * -4) + 3x * (-6 + x)) = 17
((24 + -4x) + 3x * (-6 + x)) = 17
(24 + -4x + (-6 * 3x + x * 3x)) = 17
(24 + -4x + (-18x + 3x2)) = 17

Combine like terms: -4x + -18x = -22x
(24 + -22x + 3x2) = 17

Solving
24 + -22x + 3x2 = 17

Solving for variable 'x'.

Reorder the terms:
24 + -17 + -22x + 3x2 = 17 + -17

Combine like terms: 24 + -17 = 7
7 + -22x + 3x2 = 17 + -17

Combine like terms: 17 + -17 = 0
7 + -22x + 3x2 = 0

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


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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

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 = {0.3333333333, 7}

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