2x^2+10x-6=42

Solution for 2x^2+10x-6=42 equation:

Simplifying
2x2 + 10x + -6 = 42

Reorder the terms:
-6 + 10x + 2x2 = 42

Solving
-6 + 10x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
-6 + -42 + 10x + 2x2 = 42 + -42

Combine like terms: -6 + -42 = -48
-48 + 10x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-48 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 5x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-8, 3}