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((-1 + -2x)(4 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

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

Subproblem 2

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

Solution

x = {-0.5, 4}

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