3(x^2-4)=5x(x-1)-9x

Solution for 3(x^2-4)=5x(x-1)-9x equation:

Simplifying
3(x2 + -4) = 5x(x + -1) + -9x

Reorder the terms:
3(-4 + x2) = 5x(x + -1) + -9x
(-4 * 3 + x2 * 3) = 5x(x + -1) + -9x
(-12 + 3x2) = 5x(x + -1) + -9x

Reorder the terms:
-12 + 3x2 = 5x(-1 + x) + -9x
-12 + 3x2 = (-1 * 5x + x * 5x) + -9x
-12 + 3x2 = (-5x + 5x2) + -9x

Reorder the terms:
-12 + 3x2 = -5x + -9x + 5x2

Combine like terms: -5x + -9x = -14x
-12 + 3x2 = -14x + 5x2

Solving
-12 + 3x2 = -14x + 5x2

Solving for variable 'x'.

Reorder the terms:
-12 + 14x + 3x2 + -5x2 = -14x + 5x2 + 14x + -5x2

Combine like terms: 3x2 + -5x2 = -2x2
-12 + 14x + -2x2 = -14x + 5x2 + 14x + -5x2

Reorder the terms:
-12 + 14x + -2x2 = -14x + 14x + 5x2 + -5x2

Combine like terms: -14x + 14x = 0
-12 + 14x + -2x2 = 0 + 5x2 + -5x2
-12 + 14x + -2x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-12 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 7x + -1x2) = 0

Factor a trinomial.
2((-6 + x)(1 + -1x)) = 0

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

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

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

Simplifying
x = 6
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 = {6, 1}