10x^2+35x-20=0

Solution for 10x^2+35x-20=0 equation:

Simplifying
10x2 + 35x + -20 = 0

Reorder the terms:
-20 + 35x + 10x2 = 0

Solving
-20 + 35x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 7x + 2x2) = 0

Factor a trinomial.
5((-4 + -1x)(1 + -2x)) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-4, 0.5}