(4x+2)(3x-7)=0

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Solution for (4x+2)(3x-7)=0 equation: 


Simplifying
(4x + 2)(3x + -7) = 0

Reorder the terms:
(2 + 4x)(3x + -7) = 0

Reorder the terms:
(2 + 4x)(-7 + 3x) = 0

Multiply (2 + 4x) * (-7 + 3x)
(2(-7 + 3x) + 4x * (-7 + 3x)) = 0
((-7 * 2 + 3x * 2) + 4x * (-7 + 3x)) = 0
((-14 + 6x) + 4x * (-7 + 3x)) = 0
(-14 + 6x + (-7 * 4x + 3x * 4x)) = 0
(-14 + 6x + (-28x + 12x2)) = 0

Combine like terms: 6x + -28x = -22x
(-14 + -22x + 12x2) = 0

Solving
-14 + -22x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -11x + 6x2) = 0

Factor a trinomial.
2((-1 + -2x)(7 + -3x)) = 0

Ignore the factor 2.

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 '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-0.5, 2.333333333}

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