(x-3)(3x+4)=5(x+1)+8

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Solution for (x-3)(3x+4)=5(x+1)+8 equation: 


Simplifying
(x + -3)(3x + 4) = 5(x + 1) + 8

Reorder the terms:
(-3 + x)(3x + 4) = 5(x + 1) + 8

Reorder the terms:
(-3 + x)(4 + 3x) = 5(x + 1) + 8

Multiply (-3 + x) * (4 + 3x)
(-3(4 + 3x) + x(4 + 3x)) = 5(x + 1) + 8
((4 * -3 + 3x * -3) + x(4 + 3x)) = 5(x + 1) + 8
((-12 + -9x) + x(4 + 3x)) = 5(x + 1) + 8
(-12 + -9x + (4 * x + 3x * x)) = 5(x + 1) + 8
(-12 + -9x + (4x + 3x2)) = 5(x + 1) + 8

Combine like terms: -9x + 4x = -5x
(-12 + -5x + 3x2) = 5(x + 1) + 8

Reorder the terms:
-12 + -5x + 3x2 = 5(1 + x) + 8
-12 + -5x + 3x2 = (1 * 5 + x * 5) + 8
-12 + -5x + 3x2 = (5 + 5x) + 8

Reorder the terms:
-12 + -5x + 3x2 = 5 + 8 + 5x

Combine like terms: 5 + 8 = 13
-12 + -5x + 3x2 = 13 + 5x

Solving
-12 + -5x + 3x2 = 13 + 5x

Solving for variable 'x'.

Reorder the terms:
-12 + -13 + -5x + -5x + 3x2 = 13 + 5x + -13 + -5x

Combine like terms: -12 + -13 = -25
-25 + -5x + -5x + 3x2 = 13 + 5x + -13 + -5x

Combine like terms: -5x + -5x = -10x
-25 + -10x + 3x2 = 13 + 5x + -13 + -5x

Reorder the terms:
-25 + -10x + 3x2 = 13 + -13 + 5x + -5x

Combine like terms: 13 + -13 = 0
-25 + -10x + 3x2 = 0 + 5x + -5x
-25 + -10x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-25 + -10x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1.666666667, 5}

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