(x-5)(3x+8)=(x+10)(x-4)

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Solution for (x-5)(3x+8)=(x+10)(x-4) equation: 


Simplifying
(x + -5)(3x + 8) = (x + 10)(x + -4)

Reorder the terms:
(-5 + x)(3x + 8) = (x + 10)(x + -4)

Reorder the terms:
(-5 + x)(8 + 3x) = (x + 10)(x + -4)

Multiply (-5 + x) * (8 + 3x)
(-5(8 + 3x) + x(8 + 3x)) = (x + 10)(x + -4)
((8 * -5 + 3x * -5) + x(8 + 3x)) = (x + 10)(x + -4)
((-40 + -15x) + x(8 + 3x)) = (x + 10)(x + -4)
(-40 + -15x + (8 * x + 3x * x)) = (x + 10)(x + -4)
(-40 + -15x + (8x + 3x2)) = (x + 10)(x + -4)

Combine like terms: -15x + 8x = -7x
(-40 + -7x + 3x2) = (x + 10)(x + -4)

Reorder the terms:
-40 + -7x + 3x2 = (10 + x)(x + -4)

Reorder the terms:
-40 + -7x + 3x2 = (10 + x)(-4 + x)

Multiply (10 + x) * (-4 + x)
-40 + -7x + 3x2 = (10(-4 + x) + x(-4 + x))
-40 + -7x + 3x2 = ((-4 * 10 + x * 10) + x(-4 + x))
-40 + -7x + 3x2 = ((-40 + 10x) + x(-4 + x))
-40 + -7x + 3x2 = (-40 + 10x + (-4 * x + x * x))
-40 + -7x + 3x2 = (-40 + 10x + (-4x + x2))

Combine like terms: 10x + -4x = 6x
-40 + -7x + 3x2 = (-40 + 6x + x2)

Add '40' to each side of the equation.
-40 + -7x + 40 + 3x2 = -40 + 6x + 40 + x2

Reorder the terms:
-40 + 40 + -7x + 3x2 = -40 + 6x + 40 + x2

Combine like terms: -40 + 40 = 0
0 + -7x + 3x2 = -40 + 6x + 40 + x2
-7x + 3x2 = -40 + 6x + 40 + x2

Reorder the terms:
-7x + 3x2 = -40 + 40 + 6x + x2

Combine like terms: -40 + 40 = 0
-7x + 3x2 = 0 + 6x + x2
-7x + 3x2 = 6x + x2

Solving
-7x + 3x2 = 6x + x2

Solving for variable 'x'.

Reorder the terms:
-7x + -6x + 3x2 + -1x2 = 6x + x2 + -6x + -1x2

Combine like terms: -7x + -6x = -13x
-13x + 3x2 + -1x2 = 6x + x2 + -6x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-13x + 2x2 = 6x + x2 + -6x + -1x2

Reorder the terms:
-13x + 2x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-13x + 2x2 = 0 + x2 + -1x2
-13x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-13x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-13 + 2x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-13 + 2x)' equal to zero and attempt to solve:

Simplifying
-13 + 2x = 0

Solving
-13 + 2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 2x = 0 + 13
2x = 0 + 13

Combine like terms: 0 + 13 = 13
2x = 13

Divide each side by '2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {0, 6.5}

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