(x-8)(5x+6)=(x-10)(4x+3)

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Solution for (x-8)(5x+6)=(x-10)(4x+3) equation: 


Simplifying
(x + -8)(5x + 6) = (x + -10)(4x + 3)

Reorder the terms:
(-8 + x)(5x + 6) = (x + -10)(4x + 3)

Reorder the terms:
(-8 + x)(6 + 5x) = (x + -10)(4x + 3)

Multiply (-8 + x) * (6 + 5x)
(-8(6 + 5x) + x(6 + 5x)) = (x + -10)(4x + 3)
((6 * -8 + 5x * -8) + x(6 + 5x)) = (x + -10)(4x + 3)
((-48 + -40x) + x(6 + 5x)) = (x + -10)(4x + 3)
(-48 + -40x + (6 * x + 5x * x)) = (x + -10)(4x + 3)
(-48 + -40x + (6x + 5x2)) = (x + -10)(4x + 3)

Combine like terms: -40x + 6x = -34x
(-48 + -34x + 5x2) = (x + -10)(4x + 3)

Reorder the terms:
-48 + -34x + 5x2 = (-10 + x)(4x + 3)

Reorder the terms:
-48 + -34x + 5x2 = (-10 + x)(3 + 4x)

Multiply (-10 + x) * (3 + 4x)
-48 + -34x + 5x2 = (-10(3 + 4x) + x(3 + 4x))
-48 + -34x + 5x2 = ((3 * -10 + 4x * -10) + x(3 + 4x))
-48 + -34x + 5x2 = ((-30 + -40x) + x(3 + 4x))
-48 + -34x + 5x2 = (-30 + -40x + (3 * x + 4x * x))
-48 + -34x + 5x2 = (-30 + -40x + (3x + 4x2))

Combine like terms: -40x + 3x = -37x
-48 + -34x + 5x2 = (-30 + -37x + 4x2)

Solving
-48 + -34x + 5x2 = -30 + -37x + 4x2

Solving for variable 'x'.

Reorder the terms:
-48 + 30 + -34x + 37x + 5x2 + -4x2 = -30 + -37x + 4x2 + 30 + 37x + -4x2

Combine like terms: -48 + 30 = -18
-18 + -34x + 37x + 5x2 + -4x2 = -30 + -37x + 4x2 + 30 + 37x + -4x2

Combine like terms: -34x + 37x = 3x
-18 + 3x + 5x2 + -4x2 = -30 + -37x + 4x2 + 30 + 37x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-18 + 3x + 1x2 = -30 + -37x + 4x2 + 30 + 37x + -4x2

Reorder the terms:
-18 + 3x + 1x2 = -30 + 30 + -37x + 37x + 4x2 + -4x2

Combine like terms: -30 + 30 = 0
-18 + 3x + 1x2 = 0 + -37x + 37x + 4x2 + -4x2
-18 + 3x + 1x2 = -37x + 37x + 4x2 + -4x2

Combine like terms: -37x + 37x = 0
-18 + 3x + 1x2 = 0 + 4x2 + -4x2
-18 + 3x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-18 + 3x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-6, 3}

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