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

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


Simplifying
5(x + -2) = 4(x2 + 2x + -8) + 3(x + 4)

Reorder the terms:
5(-2 + x) = 4(x2 + 2x + -8) + 3(x + 4)
(-2 * 5 + x * 5) = 4(x2 + 2x + -8) + 3(x + 4)
(-10 + 5x) = 4(x2 + 2x + -8) + 3(x + 4)

Reorder the terms:
-10 + 5x = 4(-8 + 2x + x2) + 3(x + 4)
-10 + 5x = (-8 * 4 + 2x * 4 + x2 * 4) + 3(x + 4)
-10 + 5x = (-32 + 8x + 4x2) + 3(x + 4)

Reorder the terms:
-10 + 5x = -32 + 8x + 4x2 + 3(4 + x)
-10 + 5x = -32 + 8x + 4x2 + (4 * 3 + x * 3)
-10 + 5x = -32 + 8x + 4x2 + (12 + 3x)

Reorder the terms:
-10 + 5x = -32 + 12 + 8x + 3x + 4x2

Combine like terms: -32 + 12 = -20
-10 + 5x = -20 + 8x + 3x + 4x2

Combine like terms: 8x + 3x = 11x
-10 + 5x = -20 + 11x + 4x2

Solving
-10 + 5x = -20 + 11x + 4x2

Solving for variable 'x'.

Reorder the terms:
-10 + 20 + 5x + -11x + -4x2 = -20 + 11x + 4x2 + 20 + -11x + -4x2

Combine like terms: -10 + 20 = 10
10 + 5x + -11x + -4x2 = -20 + 11x + 4x2 + 20 + -11x + -4x2

Combine like terms: 5x + -11x = -6x
10 + -6x + -4x2 = -20 + 11x + 4x2 + 20 + -11x + -4x2

Reorder the terms:
10 + -6x + -4x2 = -20 + 20 + 11x + -11x + 4x2 + -4x2

Combine like terms: -20 + 20 = 0
10 + -6x + -4x2 = 0 + 11x + -11x + 4x2 + -4x2
10 + -6x + -4x2 = 11x + -11x + 4x2 + -4x2

Combine like terms: 11x + -11x = 0
10 + -6x + -4x2 = 0 + 4x2 + -4x2
10 + -6x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
10 + -6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -3x + -2x2) = 0

Factor a trinomial.
2((1 + -1x)(5 + 2x)) = 0

Ignore the factor 2.

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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {1, -2.5}

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