3x^2-3x=3(x+15)

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Solution for 3x^2-3x=3(x+15) equation:


Simplifying
3x2 + -3x = 3(x + 15)

Reorder the terms:
-3x + 3x2 = 3(x + 15)

Reorder the terms:
-3x + 3x2 = 3(15 + x)
-3x + 3x2 = (15 * 3 + x * 3)
-3x + 3x2 = (45 + 3x)

Solving
-3x + 3x2 = 45 + 3x

Solving for variable 'x'.

Reorder the terms:
-45 + -3x + -3x + 3x2 = 45 + 3x + -45 + -3x

Combine like terms: -3x + -3x = -6x
-45 + -6x + 3x2 = 45 + 3x + -45 + -3x

Reorder the terms:
-45 + -6x + 3x2 = 45 + -45 + 3x + -3x

Combine like terms: 45 + -45 = 0
-45 + -6x + 3x2 = 0 + 3x + -3x
-45 + -6x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-45 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -2x + x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

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 = {-3, 5}

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