4r+10r^2-14=0

Solution for 4r+10r^2-14=0 equation:

Simplifying
4r + 10r2 + -14 = 0

Reorder the terms:
-14 + 4r + 10r2 = 0

Solving
-14 + 4r + 10r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 2r + 5r2) = 0

Factor a trinomial.
2((-7 + -5r)(1 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -5r)' equal to zero and attempt to solve:

Simplifying
-7 + -5r = 0

Solving
-7 + -5r = 0

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

Add '7' to each side of the equation.
-7 + 7 + -5r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5r = 0 + 7
-5r = 0 + 7

Combine like terms: 0 + 7 = 7
-5r = 7

Divide each side by '-5'.
r = -1.4

Simplifying
r = -1.4
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1r = 0 + -1
-1r = 0 + -1

Combine like terms: 0 + -1 = -1
-1r = -1

Divide each side by '-1'.
r = 1

Simplifying
r = 1
Solution
r = {-1.4, 1}