(2x+3)(3x+2)=175

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Solution for (2x+3)(3x+2)=175 equation: 


Simplifying
(2x + 3)(3x + 2) = 175

Reorder the terms:
(3 + 2x)(3x + 2) = 175

Reorder the terms:
(3 + 2x)(2 + 3x) = 175

Multiply (3 + 2x) * (2 + 3x)
(3(2 + 3x) + 2x * (2 + 3x)) = 175
((2 * 3 + 3x * 3) + 2x * (2 + 3x)) = 175
((6 + 9x) + 2x * (2 + 3x)) = 175
(6 + 9x + (2 * 2x + 3x * 2x)) = 175
(6 + 9x + (4x + 6x2)) = 175

Combine like terms: 9x + 4x = 13x
(6 + 13x + 6x2) = 175

Solving
6 + 13x + 6x2 = 175

Solving for variable 'x'.

Reorder the terms:
6 + -175 + 13x + 6x2 = 175 + -175

Combine like terms: 6 + -175 = -169
-169 + 13x + 6x2 = 175 + -175

Combine like terms: 175 + -175 = 0
-169 + 13x + 6x2 = 0

Factor a trinomial.
(-13 + -2x)(13 + -3x) = 0


Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5

Subproblem 2
Set the factor '(13 + -3x)' equal to zero and attempt to solve:

Simplifying
13 + -3x = 0

Solving
13 + -3x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -3x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -3x = 0 + -13
-3x = 0 + -13

Combine like terms: 0 + -13 = -13
-3x = -13

Divide each side by '-3'.
x = 4.333333333

Simplifying
x = 4.333333333
Solution
x = {-6.5, 4.333333333}

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