(4x-1)(x+4)=2(3x-2)

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Solution for (4x-1)(x+4)=2(3x-2) equation: 


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

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

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

Multiply (-1 + 4x) * (4 + x)
(-1(4 + x) + 4x * (4 + x)) = 2(3x + -2)
((4 * -1 + x * -1) + 4x * (4 + x)) = 2(3x + -2)
((-4 + -1x) + 4x * (4 + x)) = 2(3x + -2)
(-4 + -1x + (4 * 4x + x * 4x)) = 2(3x + -2)
(-4 + -1x + (16x + 4x2)) = 2(3x + -2)

Combine like terms: -1x + 16x = 15x
(-4 + 15x + 4x2) = 2(3x + -2)

Reorder the terms:
-4 + 15x + 4x2 = 2(-2 + 3x)
-4 + 15x + 4x2 = (-2 * 2 + 3x * 2)
-4 + 15x + 4x2 = (-4 + 6x)

Add '4' to each side of the equation.
-4 + 15x + 4 + 4x2 = -4 + 4 + 6x

Reorder the terms:
-4 + 4 + 15x + 4x2 = -4 + 4 + 6x

Combine like terms: -4 + 4 = 0
0 + 15x + 4x2 = -4 + 4 + 6x
15x + 4x2 = -4 + 4 + 6x

Combine like terms: -4 + 4 = 0
15x + 4x2 = 0 + 6x
15x + 4x2 = 6x

Solving
15x + 4x2 = 6x

Solving for variable 'x'.

Reorder the terms:
15x + -6x + 4x2 = 6x + -6x

Combine like terms: 15x + -6x = 9x
9x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
9x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + 4x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(9 + 4x)' equal to zero and attempt to solve:

Simplifying
9 + 4x = 0

Solving
9 + 4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4x = 0 + -9
4x = 0 + -9

Combine like terms: 0 + -9 = -9
4x = -9

Divide each side by '4'.
x = -2.25

Simplifying
x = -2.25
Solution
x = {0, -2.25}

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