0=4x^2-10x-6

Solution for 0=4x^2-10x-6 equation:

Simplifying
0 = 4x2 + -10x + -6

Reorder the terms:
0 = -6 + -10x + 4x2

Solving
0 = -6 + -10x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 6 = 6
6 + 10x + -4x2 = -6 + -10x + 4x2 + 6 + 10x + -4x2

Reorder the terms:
6 + 10x + -4x2 = -6 + 6 + -10x + 10x + 4x2 + -4x2

Combine like terms: -6 + 6 = 0
6 + 10x + -4x2 = 0 + -10x + 10x + 4x2 + -4x2
6 + 10x + -4x2 = -10x + 10x + 4x2 + -4x2

Combine like terms: -10x + 10x = 0
6 + 10x + -4x2 = 0 + 4x2 + -4x2
6 + 10x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + 10x + -4x2 = 0

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

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

Ignore the factor 2.
Subproblem 1
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
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 = {3, -0.5}