5x-(x+4)=10-2x(x-8)

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Solution for 5x-(x+4)=10-2x(x-8) equation: 


Simplifying
5x + -1(x + 4) = 10 + -2x(x + -8)

Reorder the terms:
5x + -1(4 + x) = 10 + -2x(x + -8)
5x + (4 * -1 + x * -1) = 10 + -2x(x + -8)
5x + (-4 + -1x) = 10 + -2x(x + -8)

Reorder the terms:
-4 + 5x + -1x = 10 + -2x(x + -8)

Combine like terms: 5x + -1x = 4x
-4 + 4x = 10 + -2x(x + -8)

Reorder the terms:
-4 + 4x = 10 + -2x(-8 + x)
-4 + 4x = 10 + (-8 * -2x + x * -2x)
-4 + 4x = 10 + (16x + -2x2)

Solving
-4 + 4x = 10 + 16x + -2x2

Solving for variable 'x'.

Reorder the terms:
-4 + -10 + 4x + -16x + 2x2 = 10 + 16x + -2x2 + -10 + -16x + 2x2

Combine like terms: -4 + -10 = -14
-14 + 4x + -16x + 2x2 = 10 + 16x + -2x2 + -10 + -16x + 2x2

Combine like terms: 4x + -16x = -12x
-14 + -12x + 2x2 = 10 + 16x + -2x2 + -10 + -16x + 2x2

Reorder the terms:
-14 + -12x + 2x2 = 10 + -10 + 16x + -16x + -2x2 + 2x2

Combine like terms: 10 + -10 = 0
-14 + -12x + 2x2 = 0 + 16x + -16x + -2x2 + 2x2
-14 + -12x + 2x2 = 16x + -16x + -2x2 + 2x2

Combine like terms: 16x + -16x = 0
-14 + -12x + 2x2 = 0 + -2x2 + 2x2
-14 + -12x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-14 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -6x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(7 + -1x)) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1, 7}

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