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

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


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

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

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

Multiply (14 + 4x) * (-4 + 3x)
(14(-4 + 3x) + 4x * (-4 + 3x)) = 0
((-4 * 14 + 3x * 14) + 4x * (-4 + 3x)) = 0
((-56 + 42x) + 4x * (-4 + 3x)) = 0
(-56 + 42x + (-4 * 4x + 3x * 4x)) = 0
(-56 + 42x + (-16x + 12x2)) = 0

Combine like terms: 42x + -16x = 26x
(-56 + 26x + 12x2) = 0

Solving
-56 + 26x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 13x + 6x2) = 0

Factor a trinomial.
2((-7 + -2x)(4 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-3.5, 1.333333333}

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