-9(x-3)-10(x+8)=4(x+8)(x-3)

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Solution for -9(x-3)-10(x+8)=4(x+8)(x-3) equation: 


Simplifying
-9(x + -3) + -10(x + 8) = 4(x + 8)(x + -3)

Reorder the terms:
-9(-3 + x) + -10(x + 8) = 4(x + 8)(x + -3)
(-3 * -9 + x * -9) + -10(x + 8) = 4(x + 8)(x + -3)
(27 + -9x) + -10(x + 8) = 4(x + 8)(x + -3)

Reorder the terms:
27 + -9x + -10(8 + x) = 4(x + 8)(x + -3)
27 + -9x + (8 * -10 + x * -10) = 4(x + 8)(x + -3)
27 + -9x + (-80 + -10x) = 4(x + 8)(x + -3)

Reorder the terms:
27 + -80 + -9x + -10x = 4(x + 8)(x + -3)

Combine like terms: 27 + -80 = -53
-53 + -9x + -10x = 4(x + 8)(x + -3)

Combine like terms: -9x + -10x = -19x
-53 + -19x = 4(x + 8)(x + -3)

Reorder the terms:
-53 + -19x = 4(8 + x)(x + -3)

Reorder the terms:
-53 + -19x = 4(8 + x)(-3 + x)

Multiply (8 + x) * (-3 + x)
-53 + -19x = 4(8(-3 + x) + x(-3 + x))
-53 + -19x = 4((-3 * 8 + x * 8) + x(-3 + x))
-53 + -19x = 4((-24 + 8x) + x(-3 + x))
-53 + -19x = 4(-24 + 8x + (-3 * x + x * x))
-53 + -19x = 4(-24 + 8x + (-3x + x2))

Combine like terms: 8x + -3x = 5x
-53 + -19x = 4(-24 + 5x + x2)
-53 + -19x = (-24 * 4 + 5x * 4 + x2 * 4)
-53 + -19x = (-96 + 20x + 4x2)

Solving
-53 + -19x = -96 + 20x + 4x2

Solving for variable 'x'.

Reorder the terms:
-53 + 96 + -19x + -20x + -4x2 = -96 + 20x + 4x2 + 96 + -20x + -4x2

Combine like terms: -53 + 96 = 43
43 + -19x + -20x + -4x2 = -96 + 20x + 4x2 + 96 + -20x + -4x2

Combine like terms: -19x + -20x = -39x
43 + -39x + -4x2 = -96 + 20x + 4x2 + 96 + -20x + -4x2

Reorder the terms:
43 + -39x + -4x2 = -96 + 96 + 20x + -20x + 4x2 + -4x2

Combine like terms: -96 + 96 = 0
43 + -39x + -4x2 = 0 + 20x + -20x + 4x2 + -4x2
43 + -39x + -4x2 = 20x + -20x + 4x2 + -4x2

Combine like terms: 20x + -20x = 0
43 + -39x + -4x2 = 0 + 4x2 + -4x2
43 + -39x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
43 + -39x + -4x2 = 0

Factor a trinomial.
(1 + -1x)(43 + 4x) = 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 '(43 + 4x)' equal to zero and attempt to solve:

Simplifying
43 + 4x = 0

Solving
43 + 4x = 0

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

Add '-43' to each side of the equation.
43 + -43 + 4x = 0 + -43

Combine like terms: 43 + -43 = 0
0 + 4x = 0 + -43
4x = 0 + -43

Combine like terms: 0 + -43 = -43
4x = -43

Divide each side by '4'.
x = -10.75

Simplifying
x = -10.75
Solution
x = {1, -10.75}

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