3x(x-8)+2(x-7)=2

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Solution for 3x(x-8)+2(x-7)=2 equation: 


Simplifying
3x(x + -8) + 2(x + -7) = 2

Reorder the terms:
3x(-8 + x) + 2(x + -7) = 2
(-8 * 3x + x * 3x) + 2(x + -7) = 2
(-24x + 3x2) + 2(x + -7) = 2

Reorder the terms:
-24x + 3x2 + 2(-7 + x) = 2
-24x + 3x2 + (-7 * 2 + x * 2) = 2
-24x + 3x2 + (-14 + 2x) = 2

Reorder the terms:
-14 + -24x + 2x + 3x2 = 2

Combine like terms: -24x + 2x = -22x
-14 + -22x + 3x2 = 2

Solving
-14 + -22x + 3x2 = 2

Solving for variable 'x'.

Reorder the terms:
-14 + -2 + -22x + 3x2 = 2 + -2

Combine like terms: -14 + -2 = -16
-16 + -22x + 3x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-16 + -22x + 3x2 = 0

Factor a trinomial.
(-2 + -3x)(8 + -1x) = 0


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

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-0.6666666667, 8}

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