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

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


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

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

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

Multiply (-4 + 5x) * (8 + x)
(-4(8 + x) + 5x * (8 + x)) = (x + 10)(4x + -3)
((8 * -4 + x * -4) + 5x * (8 + x)) = (x + 10)(4x + -3)
((-32 + -4x) + 5x * (8 + x)) = (x + 10)(4x + -3)
(-32 + -4x + (8 * 5x + x * 5x)) = (x + 10)(4x + -3)
(-32 + -4x + (40x + 5x2)) = (x + 10)(4x + -3)

Combine like terms: -4x + 40x = 36x
(-32 + 36x + 5x2) = (x + 10)(4x + -3)

Reorder the terms:
-32 + 36x + 5x2 = (10 + x)(4x + -3)

Reorder the terms:
-32 + 36x + 5x2 = (10 + x)(-3 + 4x)

Multiply (10 + x) * (-3 + 4x)
-32 + 36x + 5x2 = (10(-3 + 4x) + x(-3 + 4x))
-32 + 36x + 5x2 = ((-3 * 10 + 4x * 10) + x(-3 + 4x))
-32 + 36x + 5x2 = ((-30 + 40x) + x(-3 + 4x))
-32 + 36x + 5x2 = (-30 + 40x + (-3 * x + 4x * x))
-32 + 36x + 5x2 = (-30 + 40x + (-3x + 4x2))

Combine like terms: 40x + -3x = 37x
-32 + 36x + 5x2 = (-30 + 37x + 4x2)

Solving
-32 + 36x + 5x2 = -30 + 37x + 4x2

Solving for variable 'x'.

Reorder the terms:
-32 + 30 + 36x + -37x + 5x2 + -4x2 = -30 + 37x + 4x2 + 30 + -37x + -4x2

Combine like terms: -32 + 30 = -2
-2 + 36x + -37x + 5x2 + -4x2 = -30 + 37x + 4x2 + 30 + -37x + -4x2

Combine like terms: 36x + -37x = -1x
-2 + -1x + 5x2 + -4x2 = -30 + 37x + 4x2 + 30 + -37x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
-2 + -1x + 1x2 = -30 + 37x + 4x2 + 30 + -37x + -4x2

Reorder the terms:
-2 + -1x + 1x2 = -30 + 30 + 37x + -37x + 4x2 + -4x2

Combine like terms: -30 + 30 = 0
-2 + -1x + 1x2 = 0 + 37x + -37x + 4x2 + -4x2
-2 + -1x + 1x2 = 37x + -37x + 4x2 + -4x2

Combine like terms: 37x + -37x = 0
-2 + -1x + 1x2 = 0 + 4x2 + -4x2
-2 + -1x + 1x2 = 4x2 + -4x2

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

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


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
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
Solution
x = {-1, 2}

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