(x+5)(3x-4)=(x+8)(2x-1)

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Solution for (x+5)(3x-4)=(x+8)(2x-1) equation: 


Simplifying
(x + 5)(3x + -4) = (x + 8)(2x + -1)

Reorder the terms:
(5 + x)(3x + -4) = (x + 8)(2x + -1)

Reorder the terms:
(5 + x)(-4 + 3x) = (x + 8)(2x + -1)

Multiply (5 + x) * (-4 + 3x)
(5(-4 + 3x) + x(-4 + 3x)) = (x + 8)(2x + -1)
((-4 * 5 + 3x * 5) + x(-4 + 3x)) = (x + 8)(2x + -1)
((-20 + 15x) + x(-4 + 3x)) = (x + 8)(2x + -1)
(-20 + 15x + (-4 * x + 3x * x)) = (x + 8)(2x + -1)
(-20 + 15x + (-4x + 3x2)) = (x + 8)(2x + -1)

Combine like terms: 15x + -4x = 11x
(-20 + 11x + 3x2) = (x + 8)(2x + -1)

Reorder the terms:
-20 + 11x + 3x2 = (8 + x)(2x + -1)

Reorder the terms:
-20 + 11x + 3x2 = (8 + x)(-1 + 2x)

Multiply (8 + x) * (-1 + 2x)
-20 + 11x + 3x2 = (8(-1 + 2x) + x(-1 + 2x))
-20 + 11x + 3x2 = ((-1 * 8 + 2x * 8) + x(-1 + 2x))
-20 + 11x + 3x2 = ((-8 + 16x) + x(-1 + 2x))
-20 + 11x + 3x2 = (-8 + 16x + (-1 * x + 2x * x))
-20 + 11x + 3x2 = (-8 + 16x + (-1x + 2x2))

Combine like terms: 16x + -1x = 15x
-20 + 11x + 3x2 = (-8 + 15x + 2x2)

Solving
-20 + 11x + 3x2 = -8 + 15x + 2x2

Solving for variable 'x'.

Reorder the terms:
-20 + 8 + 11x + -15x + 3x2 + -2x2 = -8 + 15x + 2x2 + 8 + -15x + -2x2

Combine like terms: -20 + 8 = -12
-12 + 11x + -15x + 3x2 + -2x2 = -8 + 15x + 2x2 + 8 + -15x + -2x2

Combine like terms: 11x + -15x = -4x
-12 + -4x + 3x2 + -2x2 = -8 + 15x + 2x2 + 8 + -15x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-12 + -4x + 1x2 = -8 + 15x + 2x2 + 8 + -15x + -2x2

Reorder the terms:
-12 + -4x + 1x2 = -8 + 8 + 15x + -15x + 2x2 + -2x2

Combine like terms: -8 + 8 = 0
-12 + -4x + 1x2 = 0 + 15x + -15x + 2x2 + -2x2
-12 + -4x + 1x2 = 15x + -15x + 2x2 + -2x2

Combine like terms: 15x + -15x = 0
-12 + -4x + 1x2 = 0 + 2x2 + -2x2
-12 + -4x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-12 + -4x + 1x2 = 0

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


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 6}

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