(3x-7)(x+1)=8

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Solution for (3x-7)(x+1)=8 equation: 


Simplifying
(3x + -7)(x + 1) = 8

Reorder the terms:
(-7 + 3x)(x + 1) = 8

Reorder the terms:
(-7 + 3x)(1 + x) = 8

Multiply (-7 + 3x) * (1 + x)
(-7(1 + x) + 3x * (1 + x)) = 8
((1 * -7 + x * -7) + 3x * (1 + x)) = 8
((-7 + -7x) + 3x * (1 + x)) = 8
(-7 + -7x + (1 * 3x + x * 3x)) = 8
(-7 + -7x + (3x + 3x2)) = 8

Combine like terms: -7x + 3x = -4x
(-7 + -4x + 3x2) = 8

Solving
-7 + -4x + 3x2 = 8

Solving for variable 'x'.

Reorder the terms:
-7 + -8 + -4x + 3x2 = 8 + -8

Combine like terms: -7 + -8 = -15
-15 + -4x + 3x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-15 + -4x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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 = {-1.666666667, 3}

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