4x(7+2x)-(2+4x)=12

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Solution for 4x(7+2x)-(2+4x)=12 equation: 


Simplifying
4x(7 + 2x) + -1(2 + 4x) = 12
(7 * 4x + 2x * 4x) + -1(2 + 4x) = 12
(28x + 8x2) + -1(2 + 4x) = 12
28x + 8x2 + (2 * -1 + 4x * -1) = 12
28x + 8x2 + (-2 + -4x) = 12

Reorder the terms:
-2 + 28x + -4x + 8x2 = 12

Combine like terms: 28x + -4x = 24x
-2 + 24x + 8x2 = 12

Solving
-2 + 24x + 8x2 = 12

Solving for variable 'x'.

Reorder the terms:
-2 + -12 + 24x + 8x2 = 12 + -12

Combine like terms: -2 + -12 = -14
-14 + 24x + 8x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-14 + 24x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 12x + 4x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, 0.5}

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