(3x+14)(4x-9)=0

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Solution for (3x+14)(4x-9)=0 equation: 


Simplifying
(3x + 14)(4x + -9) = 0

Reorder the terms:
(14 + 3x)(4x + -9) = 0

Reorder the terms:
(14 + 3x)(-9 + 4x) = 0

Multiply (14 + 3x) * (-9 + 4x)
(14(-9 + 4x) + 3x * (-9 + 4x)) = 0
((-9 * 14 + 4x * 14) + 3x * (-9 + 4x)) = 0
((-126 + 56x) + 3x * (-9 + 4x)) = 0
(-126 + 56x + (-9 * 3x + 4x * 3x)) = 0
(-126 + 56x + (-27x + 12x2)) = 0

Combine like terms: 56x + -27x = 29x
(-126 + 29x + 12x2) = 0

Solving
-126 + 29x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-14 + -3x)(9 + -4x) = 0


Subproblem 1
Set the factor '(-14 + -3x)' equal to zero and attempt to solve:

Simplifying
-14 + -3x = 0

Solving
-14 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '14' to each side of the equation.
-14 + 14 + -3x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -3x = 0 + 14
-3x = 0 + 14

Combine like terms: 0 + 14 = 14
-3x = 14

Divide each side by '-3'.
x = -4.666666667

Simplifying
x = -4.666666667

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {-4.666666667, 2.25}

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