(3x+4)(-2x+5)=0

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Solution for (3x+4)(-2x+5)=0 equation: 


Simplifying
(3x + 4)(-2x + 5) = 0

Reorder the terms:
(4 + 3x)(-2x + 5) = 0

Reorder the terms:
(4 + 3x)(5 + -2x) = 0

Multiply (4 + 3x) * (5 + -2x)
(4(5 + -2x) + 3x * (5 + -2x)) = 0
((5 * 4 + -2x * 4) + 3x * (5 + -2x)) = 0
((20 + -8x) + 3x * (5 + -2x)) = 0
(20 + -8x + (5 * 3x + -2x * 3x)) = 0
(20 + -8x + (15x + -6x2)) = 0

Combine like terms: -8x + 15x = 7x
(20 + 7x + -6x2) = 0

Solving
20 + 7x + -6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -2x)(4 + 3x) = 0


Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

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 = {2.5, -1.333333333}

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