6x(2x+7)=54

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Solution for 6x(2x+7)=54 equation:


Simplifying
6x(2x + 7) = 54

Reorder the terms:
6x(7 + 2x) = 54
(7 * 6x + 2x * 6x) = 54
(42x + 12x2) = 54

Solving
42x + 12x2 = 54

Solving for variable 'x'.

Reorder the terms:
-54 + 42x + 12x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 42x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-9 + 7x + 2x2) = 0

Factor a trinomial.
6((-9 + -2x)(1 + -1x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 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 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5

Subproblem 2

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

Solution

x = {-4.5, 1}

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