3(2x-5)=x*x-15

Solution for 3(2x-5)=x*x-15 equation:

Simplifying
3(2x + -5) = x * x + -15

Reorder the terms:
3(-5 + 2x) = x * x + -15
(-5 * 3 + 2x * 3) = x * x + -15
(-15 + 6x) = x * x + -15

Multiply x * x
-15 + 6x = x2 + -15

Reorder the terms:
-15 + 6x = -15 + x2

Add '15' to each side of the equation.
-15 + 15 + 6x = -15 + 15 + x2

Combine like terms: -15 + 15 = 0
0 + 6x = -15 + 15 + x2
6x = -15 + 15 + x2

Combine like terms: -15 + 15 = 0
6x = 0 + x2
6x = x2

Solving
6x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
6x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + -1x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 6}