3(x-1)(x+3)=51+3x

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Solution for 3(x-1)(x+3)=51+3x equation: 


Simplifying
3(x + -1)(x + 3) = 51 + 3x

Reorder the terms:
3(-1 + x)(x + 3) = 51 + 3x

Reorder the terms:
3(-1 + x)(3 + x) = 51 + 3x

Multiply (-1 + x) * (3 + x)
3(-1(3 + x) + x(3 + x)) = 51 + 3x
3((3 * -1 + x * -1) + x(3 + x)) = 51 + 3x
3((-3 + -1x) + x(3 + x)) = 51 + 3x
3(-3 + -1x + (3 * x + x * x)) = 51 + 3x
3(-3 + -1x + (3x + x2)) = 51 + 3x

Combine like terms: -1x + 3x = 2x
3(-3 + 2x + x2) = 51 + 3x
(-3 * 3 + 2x * 3 + x2 * 3) = 51 + 3x
(-9 + 6x + 3x2) = 51 + 3x

Solving
-9 + 6x + 3x2 = 51 + 3x

Solving for variable 'x'.

Reorder the terms:
-9 + -51 + 6x + -3x + 3x2 = 51 + 3x + -51 + -3x

Combine like terms: -9 + -51 = -60
-60 + 6x + -3x + 3x2 = 51 + 3x + -51 + -3x

Combine like terms: 6x + -3x = 3x
-60 + 3x + 3x2 = 51 + 3x + -51 + -3x

Reorder the terms:
-60 + 3x + 3x2 = 51 + -51 + 3x + -3x

Combine like terms: 51 + -51 = 0
-60 + 3x + 3x2 = 0 + 3x + -3x
-60 + 3x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-60 + 3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + x + x2) = 0

Factor a trinomial.
3((-5 + -1x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}

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