4x^2+30x=16

Solution for 4x^2+30x=16 equation:

Simplifying
4x2 + 30x = 16

Reorder the terms:
30x + 4x2 = 16

Solving
30x + 4x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 30x + 4x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 30x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 15x + 2x2) = 0

Factor a trinomial.
2((-8 + -1x)(1 + -2x)) = 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 '(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 = {-8, 0.5}