x(3x-15)=252

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Solution for x(3x-15)=252 equation: 


Simplifying
x(3x + -15) = 252

Reorder the terms:
x(-15 + 3x) = 252
(-15 * x + 3x * x) = 252
(-15x + 3x2) = 252

Solving
-15x + 3x2 = 252

Solving for variable 'x'.

Reorder the terms:
-252 + -15x + 3x2 = 252 + -252

Combine like terms: 252 + -252 = 0
-252 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-84 + -5x + x2) = 0

Factor a trinomial.
3((-7 + -1x)(12 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-7, 12}

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