3x(x-4)=2(x+1)+3

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Solution for 3x(x-4)=2(x+1)+3 equation: 


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

Reorder the terms:
3x(-4 + x) = 2(x + 1) + 3
(-4 * 3x + x * 3x) = 2(x + 1) + 3
(-12x + 3x2) = 2(x + 1) + 3

Reorder the terms:
-12x + 3x2 = 2(1 + x) + 3
-12x + 3x2 = (1 * 2 + x * 2) + 3
-12x + 3x2 = (2 + 2x) + 3

Reorder the terms:
-12x + 3x2 = 2 + 3 + 2x

Combine like terms: 2 + 3 = 5
-12x + 3x2 = 5 + 2x

Solving
-12x + 3x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
-5 + -12x + -2x + 3x2 = 5 + 2x + -5 + -2x

Combine like terms: -12x + -2x = -14x
-5 + -14x + 3x2 = 5 + 2x + -5 + -2x

Reorder the terms:
-5 + -14x + 3x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
-5 + -14x + 3x2 = 0 + 2x + -2x
-5 + -14x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-5 + -14x + 3x2 = 0

Factor a trinomial.
(-1 + -3x)(5 + -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 '(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 = {-0.3333333333, 5}

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