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

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


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

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

Reorder the terms:
4 + 8x = 2x(-3 + 4x)
4 + 8x = (-3 * 2x + 4x * 2x)
4 + 8x = (-6x + 8x2)

Solving
4 + 8x = -6x + 8x2

Solving for variable 'x'.

Combine like terms: 8x + 6x = 14x
4 + 14x + -8x2 = -6x + 8x2 + 6x + -8x2

Reorder the terms:
4 + 14x + -8x2 = -6x + 6x + 8x2 + -8x2

Combine like terms: -6x + 6x = 0
4 + 14x + -8x2 = 0 + 8x2 + -8x2
4 + 14x + -8x2 = 8x2 + -8x2

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

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

Factor a trinomial.
2((2 + -1x)(1 + 4x)) = 0

Ignore the factor 2.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {2, -0.25}

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