4x^2-32x+80+2x^2-28=42

Solution for 4x^2-32x+80+2x^2-28=42 equation:

Simplifying
4x2 + -32x + 80 + 2x2 + -28 = 42

Reorder the terms:
80 + -28 + -32x + 4x2 + 2x2 = 42

Combine like terms: 80 + -28 = 52
52 + -32x + 4x2 + 2x2 = 42

Combine like terms: 4x2 + 2x2 = 6x2
52 + -32x + 6x2 = 42

Solving
52 + -32x + 6x2 = 42

Solving for variable 'x'.

Reorder the terms:
52 + -42 + -32x + 6x2 = 42 + -42

Combine like terms: 52 + -42 = 10
10 + -32x + 6x2 = 42 + -42

Combine like terms: 42 + -42 = 0
10 + -32x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -16x + 3x2) = 0

Factor a trinomial.
2((1 + -3x)(5 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
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 = {0.3333333333, 5}