2x(x-3)=5-(x^2-4)

Solution for 2x(x-3)=5-(x^2-4) equation:

Simplifying
2x(x + -3) = 5 + -1(x2 + -4)

Reorder the terms:
2x(-3 + x) = 5 + -1(x2 + -4)
(-3 * 2x + x * 2x) = 5 + -1(x2 + -4)
(-6x + 2x2) = 5 + -1(x2 + -4)

Reorder the terms:
-6x + 2x2 = 5 + -1(-4 + x2)
-6x + 2x2 = 5 + (-4 * -1 + x2 * -1)
-6x + 2x2 = 5 + (4 + -1x2)

Combine like terms: 5 + 4 = 9
-6x + 2x2 = 9 + -1x2

Solving
-6x + 2x2 = 9 + -1x2

Solving for variable 'x'.

Reorder the terms:
-9 + -6x + 2x2 + x2 = 9 + -1x2 + -9 + x2

Combine like terms: 2x2 + x2 = 3x2
-9 + -6x + 3x2 = 9 + -1x2 + -9 + x2

Reorder the terms:
-9 + -6x + 3x2 = 9 + -9 + -1x2 + x2

Combine like terms: 9 + -9 = 0
-9 + -6x + 3x2 = 0 + -1x2 + x2
-9 + -6x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-9 + -6x + 3x2 = 0

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

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 3}