3(x^2-2)=(x-5)(x+1)+5

Solution for 3(x^2-2)=(x-5)(x+1)+5 equation:

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

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

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

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

Multiply (-5 + x) * (1 + x)
-6 + 3x2 = (-5(1 + x) + x(1 + x)) + 5
-6 + 3x2 = ((1 * -5 + x * -5) + x(1 + x)) + 5
-6 + 3x2 = ((-5 + -5x) + x(1 + x)) + 5
-6 + 3x2 = (-5 + -5x + (1 * x + x * x)) + 5
-6 + 3x2 = (-5 + -5x + (1x + x2)) + 5

Combine like terms: -5x + 1x = -4x
-6 + 3x2 = (-5 + -4x + x2) + 5

Reorder the terms:
-6 + 3x2 = -5 + 5 + -4x + x2

Combine like terms: -5 + 5 = 0
-6 + 3x2 = 0 + -4x + x2
-6 + 3x2 = -4x + x2

Solving
-6 + 3x2 = -4x + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 4x + 3x2 + -1x2 = -4x + x2 + 4x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-6 + 4x + 2x2 = -4x + x2 + 4x + -1x2

Reorder the terms:
-6 + 4x + 2x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
-6 + 4x + 2x2 = 0 + x2 + -1x2
-6 + 4x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 4x + 2x2 = 0

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

Factor a trinomial.
2((-3 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
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 '(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
Solution
x = {-3, 1}