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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