(2x-3)(3x-2)=5(x^2-6)

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Solution for (2x-3)(3x-2)=5(x^2-6) equation: 


Simplifying
(2x + -3)(3x + -2) = 5(x2 + -6)

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

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

Multiply (-3 + 2x) * (-2 + 3x)
(-3(-2 + 3x) + 2x * (-2 + 3x)) = 5(x2 + -6)
((-2 * -3 + 3x * -3) + 2x * (-2 + 3x)) = 5(x2 + -6)
((6 + -9x) + 2x * (-2 + 3x)) = 5(x2 + -6)
(6 + -9x + (-2 * 2x + 3x * 2x)) = 5(x2 + -6)
(6 + -9x + (-4x + 6x2)) = 5(x2 + -6)

Combine like terms: -9x + -4x = -13x
(6 + -13x + 6x2) = 5(x2 + -6)

Reorder the terms:
6 + -13x + 6x2 = 5(-6 + x2)
6 + -13x + 6x2 = (-6 * 5 + x2 * 5)
6 + -13x + 6x2 = (-30 + 5x2)

Solving
6 + -13x + 6x2 = -30 + 5x2

Solving for variable 'x'.

Reorder the terms:
6 + 30 + -13x + 6x2 + -5x2 = -30 + 5x2 + 30 + -5x2

Combine like terms: 6 + 30 = 36
36 + -13x + 6x2 + -5x2 = -30 + 5x2 + 30 + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
36 + -13x + 1x2 = -30 + 5x2 + 30 + -5x2

Reorder the terms:
36 + -13x + 1x2 = -30 + 30 + 5x2 + -5x2

Combine like terms: -30 + 30 = 0
36 + -13x + 1x2 = 0 + 5x2 + -5x2
36 + -13x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
36 + -13x + 1x2 = 0

Factor a trinomial.
(4 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {4, 9}

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