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

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


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

Reorder the terms:
4x(-3 + x) = 2x + 8
(-3 * 4x + x * 4x) = 2x + 8
(-12x + 4x2) = 2x + 8

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

Solving
-12x + 4x2 = 8 + 2x

Solving for variable 'x'.

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

Combine like terms: -12x + -2x = -14x
-8 + -14x + 4x2 = 8 + 2x + -8 + -2x

Reorder the terms:
-8 + -14x + 4x2 = 8 + -8 + 2x + -2x

Combine like terms: 8 + -8 = 0
-8 + -14x + 4x2 = 0 + 2x + -2x
-8 + -14x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-8 + -14x + 4x2 = 0

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

Factor a trinomial.
2((-1 + -2x)(4 + -1x)) = 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 '(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
Solution
x = {-0.5, 4}

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