(2x+3)(x-4)=(3x-8)(x-3)

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Solution for (2x+3)(x-4)=(3x-8)(x-3) equation: 


Simplifying
(2x + 3)(x + -4) = (3x + -8)(x + -3)

Reorder the terms:
(3 + 2x)(x + -4) = (3x + -8)(x + -3)

Reorder the terms:
(3 + 2x)(-4 + x) = (3x + -8)(x + -3)

Multiply (3 + 2x) * (-4 + x)
(3(-4 + x) + 2x * (-4 + x)) = (3x + -8)(x + -3)
((-4 * 3 + x * 3) + 2x * (-4 + x)) = (3x + -8)(x + -3)
((-12 + 3x) + 2x * (-4 + x)) = (3x + -8)(x + -3)
(-12 + 3x + (-4 * 2x + x * 2x)) = (3x + -8)(x + -3)
(-12 + 3x + (-8x + 2x2)) = (3x + -8)(x + -3)

Combine like terms: 3x + -8x = -5x
(-12 + -5x + 2x2) = (3x + -8)(x + -3)

Reorder the terms:
-12 + -5x + 2x2 = (-8 + 3x)(x + -3)

Reorder the terms:
-12 + -5x + 2x2 = (-8 + 3x)(-3 + x)

Multiply (-8 + 3x) * (-3 + x)
-12 + -5x + 2x2 = (-8(-3 + x) + 3x * (-3 + x))
-12 + -5x + 2x2 = ((-3 * -8 + x * -8) + 3x * (-3 + x))
-12 + -5x + 2x2 = ((24 + -8x) + 3x * (-3 + x))
-12 + -5x + 2x2 = (24 + -8x + (-3 * 3x + x * 3x))
-12 + -5x + 2x2 = (24 + -8x + (-9x + 3x2))

Combine like terms: -8x + -9x = -17x
-12 + -5x + 2x2 = (24 + -17x + 3x2)

Solving
-12 + -5x + 2x2 = 24 + -17x + 3x2

Solving for variable 'x'.

Reorder the terms:
-12 + -24 + -5x + 17x + 2x2 + -3x2 = 24 + -17x + 3x2 + -24 + 17x + -3x2

Combine like terms: -12 + -24 = -36
-36 + -5x + 17x + 2x2 + -3x2 = 24 + -17x + 3x2 + -24 + 17x + -3x2

Combine like terms: -5x + 17x = 12x
-36 + 12x + 2x2 + -3x2 = 24 + -17x + 3x2 + -24 + 17x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-36 + 12x + -1x2 = 24 + -17x + 3x2 + -24 + 17x + -3x2

Reorder the terms:
-36 + 12x + -1x2 = 24 + -24 + -17x + 17x + 3x2 + -3x2

Combine like terms: 24 + -24 = 0
-36 + 12x + -1x2 = 0 + -17x + 17x + 3x2 + -3x2
-36 + 12x + -1x2 = -17x + 17x + 3x2 + -3x2

Combine like terms: -17x + 17x = 0
-36 + 12x + -1x2 = 0 + 3x2 + -3x2
-36 + 12x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-36 + 12x + -1x2 = 0

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


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 '(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 = {6, 6}

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