5(x^2-7)-3x(2+x)-x(x-8)=0

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Solution for 5(x^2-7)-3x(2+x)-x(x-8)=0 equation: 


Simplifying
5(x2 + -7) + -3x(2 + x) + -1x(x + -8) = 0

Reorder the terms:
5(-7 + x2) + -3x(2 + x) + -1x(x + -8) = 0
(-7 * 5 + x2 * 5) + -3x(2 + x) + -1x(x + -8) = 0
(-35 + 5x2) + -3x(2 + x) + -1x(x + -8) = 0
-35 + 5x2 + (2 * -3x + x * -3x) + -1x(x + -8) = 0
-35 + 5x2 + (-6x + -3x2) + -1x(x + -8) = 0

Reorder the terms:
-35 + 5x2 + -6x + -3x2 + -1x(-8 + x) = 0
-35 + 5x2 + -6x + -3x2 + (-8 * -1x + x * -1x) = 0
-35 + 5x2 + -6x + -3x2 + (8x + -1x2) = 0

Reorder the terms:
-35 + -6x + 8x + 5x2 + -3x2 + -1x2 = 0

Combine like terms: -6x + 8x = 2x
-35 + 2x + 5x2 + -3x2 + -1x2 = 0

Combine like terms: 5x2 + -3x2 = 2x2
-35 + 2x + 2x2 + -1x2 = 0

Combine like terms: 2x2 + -1x2 = 1x2
-35 + 2x + 1x2 = 0

Solving
-35 + 2x + 1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -1x)(5 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-7, 5}

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