4x(x+2)=16x-3

Solution for 4x(x+2)=16x-3 equation:

Simplifying
4x(x + 2) = 16x + -3

Reorder the terms:
4x(2 + x) = 16x + -3
(2 * 4x + x * 4x) = 16x + -3
(8x + 4x2) = 16x + -3

Reorder the terms:
8x + 4x2 = -3 + 16x

Solving
8x + 4x2 = -3 + 16x

Solving for variable 'x'.

Reorder the terms:
3 + 8x + -16x + 4x2 = -3 + 16x + 3 + -16x

Combine like terms: 8x + -16x = -8x
3 + -8x + 4x2 = -3 + 16x + 3 + -16x

Reorder the terms:
3 + -8x + 4x2 = -3 + 3 + 16x + -16x

Combine like terms: -3 + 3 = 0
3 + -8x + 4x2 = 0 + 16x + -16x
3 + -8x + 4x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
3 + -8x + 4x2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0.5, 1.5}