(5x-2)(3x+4)=(3x-5)(5x+1)+15

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Solution for (5x-2)(3x+4)=(3x-5)(5x+1)+15 equation: 


Simplifying
(5x + -2)(3x + 4) = (3x + -5)(5x + 1) + 15

Reorder the terms:
(-2 + 5x)(3x + 4) = (3x + -5)(5x + 1) + 15

Reorder the terms:
(-2 + 5x)(4 + 3x) = (3x + -5)(5x + 1) + 15

Multiply (-2 + 5x) * (4 + 3x)
(-2(4 + 3x) + 5x * (4 + 3x)) = (3x + -5)(5x + 1) + 15
((4 * -2 + 3x * -2) + 5x * (4 + 3x)) = (3x + -5)(5x + 1) + 15
((-8 + -6x) + 5x * (4 + 3x)) = (3x + -5)(5x + 1) + 15
(-8 + -6x + (4 * 5x + 3x * 5x)) = (3x + -5)(5x + 1) + 15
(-8 + -6x + (20x + 15x2)) = (3x + -5)(5x + 1) + 15

Combine like terms: -6x + 20x = 14x
(-8 + 14x + 15x2) = (3x + -5)(5x + 1) + 15

Reorder the terms:
-8 + 14x + 15x2 = (-5 + 3x)(5x + 1) + 15

Reorder the terms:
-8 + 14x + 15x2 = (-5 + 3x)(1 + 5x) + 15

Multiply (-5 + 3x) * (1 + 5x)
-8 + 14x + 15x2 = (-5(1 + 5x) + 3x * (1 + 5x)) + 15
-8 + 14x + 15x2 = ((1 * -5 + 5x * -5) + 3x * (1 + 5x)) + 15
-8 + 14x + 15x2 = ((-5 + -25x) + 3x * (1 + 5x)) + 15
-8 + 14x + 15x2 = (-5 + -25x + (1 * 3x + 5x * 3x)) + 15
-8 + 14x + 15x2 = (-5 + -25x + (3x + 15x2)) + 15

Combine like terms: -25x + 3x = -22x
-8 + 14x + 15x2 = (-5 + -22x + 15x2) + 15

Reorder the terms:
-8 + 14x + 15x2 = -5 + 15 + -22x + 15x2

Combine like terms: -5 + 15 = 10
-8 + 14x + 15x2 = 10 + -22x + 15x2

Add '-15x2' to each side of the equation.
-8 + 14x + 15x2 + -15x2 = 10 + -22x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-8 + 14x + 0 = 10 + -22x + 15x2 + -15x2
-8 + 14x = 10 + -22x + 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-8 + 14x = 10 + -22x + 0
-8 + 14x = 10 + -22x

Solving
-8 + 14x = 10 + -22x

Solving for variable 'x'.

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

Add '22x' to each side of the equation.
-8 + 14x + 22x = 10 + -22x + 22x

Combine like terms: 14x + 22x = 36x
-8 + 36x = 10 + -22x + 22x

Combine like terms: -22x + 22x = 0
-8 + 36x = 10 + 0
-8 + 36x = 10

Add '8' to each side of the equation.
-8 + 8 + 36x = 10 + 8

Combine like terms: -8 + 8 = 0
0 + 36x = 10 + 8
36x = 10 + 8

Combine like terms: 10 + 8 = 18
36x = 18

Divide each side by '36'.
x = 0.5

Simplifying
x = 0.5

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