(2x+3)(x+4)=187

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Solution for (2x+3)(x+4)=187 equation: 


Simplifying
(2x + 3)(x + 4) = 187

Reorder the terms:
(3 + 2x)(x + 4) = 187

Reorder the terms:
(3 + 2x)(4 + x) = 187

Multiply (3 + 2x) * (4 + x)
(3(4 + x) + 2x * (4 + x)) = 187
((4 * 3 + x * 3) + 2x * (4 + x)) = 187
((12 + 3x) + 2x * (4 + x)) = 187
(12 + 3x + (4 * 2x + x * 2x)) = 187
(12 + 3x + (8x + 2x2)) = 187

Combine like terms: 3x + 8x = 11x
(12 + 11x + 2x2) = 187

Solving
12 + 11x + 2x2 = 187

Solving for variable 'x'.

Reorder the terms:
12 + -187 + 11x + 2x2 = 187 + -187

Combine like terms: 12 + -187 = -175
-175 + 11x + 2x2 = 187 + -187

Combine like terms: 187 + -187 = 0
-175 + 11x + 2x2 = 0

Factor a trinomial.
(-25 + -2x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-25 + -2x)' equal to zero and attempt to solve:

Simplifying
-25 + -2x = 0

Solving
-25 + -2x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -2x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2x = 0 + 25
-2x = 0 + 25

Combine like terms: 0 + 25 = 25
-2x = 25

Divide each side by '-2'.
x = -12.5

Simplifying
x = -12.5

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-12.5, 7}

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