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

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


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

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

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

Multiply (3 + 2x) * (-7 + 4x)
(3(-7 + 4x) + 2x * (-7 + 4x)) = 0
((-7 * 3 + 4x * 3) + 2x * (-7 + 4x)) = 0
((-21 + 12x) + 2x * (-7 + 4x)) = 0
(-21 + 12x + (-7 * 2x + 4x * 2x)) = 0
(-21 + 12x + (-14x + 8x2)) = 0

Combine like terms: 12x + -14x = -2x
(-21 + -2x + 8x2) = 0

Solving
-21 + -2x + 8x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-1.5, 1.75}

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