(x+5)(2x+7)-(3-2x)(2x+7)=0

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Solution for (x+5)(2x+7)-(3-2x)(2x+7)=0 equation: 


Simplifying
(x + 5)(2x + 7) + -1(3 + -2x)(2x + 7) = 0

Reorder the terms:
(5 + x)(2x + 7) + -1(3 + -2x)(2x + 7) = 0

Reorder the terms:
(5 + x)(7 + 2x) + -1(3 + -2x)(2x + 7) = 0

Multiply (5 + x) * (7 + 2x)
(5(7 + 2x) + x(7 + 2x)) + -1(3 + -2x)(2x + 7) = 0
((7 * 5 + 2x * 5) + x(7 + 2x)) + -1(3 + -2x)(2x + 7) = 0
((35 + 10x) + x(7 + 2x)) + -1(3 + -2x)(2x + 7) = 0
(35 + 10x + (7 * x + 2x * x)) + -1(3 + -2x)(2x + 7) = 0
(35 + 10x + (7x + 2x2)) + -1(3 + -2x)(2x + 7) = 0

Combine like terms: 10x + 7x = 17x
(35 + 17x + 2x2) + -1(3 + -2x)(2x + 7) = 0

Reorder the terms:
35 + 17x + 2x2 + -1(3 + -2x)(7 + 2x) = 0

Multiply (3 + -2x) * (7 + 2x)
35 + 17x + 2x2 + -1(3(7 + 2x) + -2x * (7 + 2x)) = 0
35 + 17x + 2x2 + -1((7 * 3 + 2x * 3) + -2x * (7 + 2x)) = 0
35 + 17x + 2x2 + -1((21 + 6x) + -2x * (7 + 2x)) = 0
35 + 17x + 2x2 + -1(21 + 6x + (7 * -2x + 2x * -2x)) = 0
35 + 17x + 2x2 + -1(21 + 6x + (-14x + -4x2)) = 0

Combine like terms: 6x + -14x = -8x
35 + 17x + 2x2 + -1(21 + -8x + -4x2) = 0
35 + 17x + 2x2 + (21 * -1 + -8x * -1 + -4x2 * -1) = 0
35 + 17x + 2x2 + (-21 + 8x + 4x2) = 0

Reorder the terms:
35 + -21 + 17x + 8x + 2x2 + 4x2 = 0

Combine like terms: 35 + -21 = 14
14 + 17x + 8x + 2x2 + 4x2 = 0

Combine like terms: 17x + 8x = 25x
14 + 25x + 2x2 + 4x2 = 0

Combine like terms: 2x2 + 4x2 = 6x2
14 + 25x + 6x2 = 0

Solving
14 + 25x + 6x2 = 0

Solving for variable 'x'.

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


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

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

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

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

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

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-3.5, -0.6666666667}

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