x(8x+6)=3x^2-33x+54

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Solution for x(8x+6)=3x^2-33x+54 equation:


Simplifying
x(8x + 6) = 3x2 + -33x + 54

Reorder the terms:
x(6 + 8x) = 3x2 + -33x + 54
(6 * x + 8x * x) = 3x2 + -33x + 54
(6x + 8x2) = 3x2 + -33x + 54

Reorder the terms:
6x + 8x2 = 54 + -33x + 3x2

Solving
6x + 8x2 = 54 + -33x + 3x2

Solving for variable 'x'.

Reorder the terms:
-54 + 6x + 33x + 8x2 + -3x2 = 54 + -33x + 3x2 + -54 + 33x + -3x2

Combine like terms: 6x + 33x = 39x
-54 + 39x + 8x2 + -3x2 = 54 + -33x + 3x2 + -54 + 33x + -3x2

Combine like terms: 8x2 + -3x2 = 5x2
-54 + 39x + 5x2 = 54 + -33x + 3x2 + -54 + 33x + -3x2

Reorder the terms:
-54 + 39x + 5x2 = 54 + -54 + -33x + 33x + 3x2 + -3x2

Combine like terms: 54 + -54 = 0
-54 + 39x + 5x2 = 0 + -33x + 33x + 3x2 + -3x2
-54 + 39x + 5x2 = -33x + 33x + 3x2 + -3x2

Combine like terms: -33x + 33x = 0
-54 + 39x + 5x2 = 0 + 3x2 + -3x2
-54 + 39x + 5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-54 + 39x + 5x2 = 0

Factor a trinomial.
(-9 + -1x)(6 + -5x) = 0

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 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 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2

Solution

x = {-9, 1.2}

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