3x(2x+7)=12

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Solution for 3x(2x+7)=12 equation:


Simplifying
3x(2x + 7) = 12

Reorder the terms:
3x(7 + 2x) = 12
(7 * 3x + 2x * 3x) = 12
(21x + 6x2) = 12

Solving
21x + 6x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 21x + 6x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 7x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 2

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

Solution

x = {-4, 0.5}

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