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

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


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

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

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

Solving
-1x + 4x2 = 3 + 3x

Solving for variable 'x'.

Reorder the terms:
-3 + -1x + -3x + 4x2 = 3 + 3x + -3 + -3x

Combine like terms: -1x + -3x = -4x
-3 + -4x + 4x2 = 3 + 3x + -3 + -3x

Reorder the terms:
-3 + -4x + 4x2 = 3 + -3 + 3x + -3x

Combine like terms: 3 + -3 = 0
-3 + -4x + 4x2 = 0 + 3x + -3x
-3 + -4x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-3 + -4x + 4x2 = 0

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


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}

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