(3+5x)(3+5x)-(4x-7)(3+5x)=0

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Solution for (3+5x)(3+5x)-(4x-7)(3+5x)=0 equation: 


Simplifying
(3 + 5x)(3 + 5x) + -1(4x + -7)(3 + 5x) = 0

Multiply (3 + 5x) * (3 + 5x)
(3(3 + 5x) + 5x * (3 + 5x)) + -1(4x + -7)(3 + 5x) = 0
((3 * 3 + 5x * 3) + 5x * (3 + 5x)) + -1(4x + -7)(3 + 5x) = 0
((9 + 15x) + 5x * (3 + 5x)) + -1(4x + -7)(3 + 5x) = 0
(9 + 15x + (3 * 5x + 5x * 5x)) + -1(4x + -7)(3 + 5x) = 0
(9 + 15x + (15x + 25x2)) + -1(4x + -7)(3 + 5x) = 0

Combine like terms: 15x + 15x = 30x
(9 + 30x + 25x2) + -1(4x + -7)(3 + 5x) = 0

Reorder the terms:
9 + 30x + 25x2 + -1(-7 + 4x)(3 + 5x) = 0

Multiply (-7 + 4x) * (3 + 5x)
9 + 30x + 25x2 + -1(-7(3 + 5x) + 4x * (3 + 5x)) = 0
9 + 30x + 25x2 + -1((3 * -7 + 5x * -7) + 4x * (3 + 5x)) = 0
9 + 30x + 25x2 + -1((-21 + -35x) + 4x * (3 + 5x)) = 0
9 + 30x + 25x2 + -1(-21 + -35x + (3 * 4x + 5x * 4x)) = 0
9 + 30x + 25x2 + -1(-21 + -35x + (12x + 20x2)) = 0

Combine like terms: -35x + 12x = -23x
9 + 30x + 25x2 + -1(-21 + -23x + 20x2) = 0
9 + 30x + 25x2 + (-21 * -1 + -23x * -1 + 20x2 * -1) = 0
9 + 30x + 25x2 + (21 + 23x + -20x2) = 0

Reorder the terms:
9 + 21 + 30x + 23x + 25x2 + -20x2 = 0

Combine like terms: 9 + 21 = 30
30 + 30x + 23x + 25x2 + -20x2 = 0

Combine like terms: 30x + 23x = 53x
30 + 53x + 25x2 + -20x2 = 0

Combine like terms: 25x2 + -20x2 = 5x2
30 + 53x + 5x2 = 0

Solving
30 + 53x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(10 + x)(3 + 5x) = 0


Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10

Subproblem 2
Set the factor '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

Solving
3 + 5x = 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 + 5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x = 0 + -3
5x = 0 + -3

Combine like terms: 0 + -3 = -3
5x = -3

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6
Solution
x = {-10, -0.6}

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