4x(2x+2)-(8x*2+3)=3

Solution for 4x(2x+2)-(8x*2+3)=3 equation:

Simplifying
4x(2x + 2) + -1(8x * 2 + 3) = 3

Reorder the terms:
4x(2 + 2x) + -1(8x * 2 + 3) = 3
(2 * 4x + 2x * 4x) + -1(8x * 2 + 3) = 3
(8x + 8x2) + -1(8x * 2 + 3) = 3

Reorder the terms for easier multiplication:
8x + 8x2 + -1(8 * 2x + 3) = 3

Multiply 8 * 2
8x + 8x2 + -1(16x + 3) = 3

Reorder the terms:
8x + 8x2 + -1(3 + 16x) = 3
8x + 8x2 + (3 * -1 + 16x * -1) = 3
8x + 8x2 + (-3 + -16x) = 3

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

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

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

Solving for variable 'x'.

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

Combine like terms: -3 + -3 = -6
-6 + -8x + 8x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + -8x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -4x + 4x2) = 0

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

Ignore the factor 2.
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}