4x^2+12x=16

Solution for 4x^2+12x=16 equation:

Simplifying
4x2 + 12x = 16

Reorder the terms:
12x + 4x2 = 16

Solving
12x + 4x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 12x + 4x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 3x + x2) = 0

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

Ignore the factor 4.
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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-4, 1}