4x(3x-1)=5x+66

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Solution for 4x(3x-1)=5x+66 equation: 


Simplifying
4x(3x + -1) = 5x + 66

Reorder the terms:
4x(-1 + 3x) = 5x + 66
(-1 * 4x + 3x * 4x) = 5x + 66
(-4x + 12x2) = 5x + 66

Reorder the terms:
-4x + 12x2 = 66 + 5x

Solving
-4x + 12x2 = 66 + 5x

Solving for variable 'x'.

Reorder the terms:
-66 + -4x + -5x + 12x2 = 66 + 5x + -66 + -5x

Combine like terms: -4x + -5x = -9x
-66 + -9x + 12x2 = 66 + 5x + -66 + -5x

Reorder the terms:
-66 + -9x + 12x2 = 66 + -66 + 5x + -5x

Combine like terms: 66 + -66 = 0
-66 + -9x + 12x2 = 0 + 5x + -5x
-66 + -9x + 12x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-66 + -9x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + -3x + 4x2) = 0

Factor a trinomial.
3((-2 + -1x)(11 + -4x)) = 0

Ignore the factor 3.

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 '(11 + -4x)' equal to zero and attempt to solve:

Simplifying
11 + -4x = 0

Solving
11 + -4x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4x = 0 + -11
-4x = 0 + -11

Combine like terms: 0 + -11 = -11
-4x = -11

Divide each side by '-4'.
x = 2.75

Simplifying
x = 2.75
Solution
x = {-2, 2.75}

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