3x^2-7x-160=x-5x^2

Solution for 3x^2-7x-160=x-5x^2 equation:

Simplifying
3x2 + -7x + -160 = x + -5x2

Reorder the terms:
-160 + -7x + 3x2 = x + -5x2

Solving
-160 + -7x + 3x2 = x + -5x2

Solving for variable 'x'.

Reorder the terms:
-160 + -7x + -1x + 3x2 + 5x2 = x + -5x2 + -1x + 5x2

Combine like terms: -7x + -1x = -8x
-160 + -8x + 3x2 + 5x2 = x + -5x2 + -1x + 5x2

Combine like terms: 3x2 + 5x2 = 8x2
-160 + -8x + 8x2 = x + -5x2 + -1x + 5x2

Reorder the terms:
-160 + -8x + 8x2 = x + -1x + -5x2 + 5x2

Combine like terms: x + -1x = 0
-160 + -8x + 8x2 = 0 + -5x2 + 5x2
-160 + -8x + 8x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-160 + -8x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-20 + -1x + x2) = 0

Factor a trinomial.
8((-4 + -1x)(5 + -1x)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 5}