(3x-8)(5x+7)-(3x-5)(5x+4)=0

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Solution for (3x-8)(5x+7)-(3x-5)(5x+4)=0 equation: 


Simplifying
(3x + -8)(5x + 7) + -1(3x + -5)(5x + 4) = 0

Reorder the terms:
(-8 + 3x)(5x + 7) + -1(3x + -5)(5x + 4) = 0

Reorder the terms:
(-8 + 3x)(7 + 5x) + -1(3x + -5)(5x + 4) = 0

Multiply (-8 + 3x) * (7 + 5x)
(-8(7 + 5x) + 3x * (7 + 5x)) + -1(3x + -5)(5x + 4) = 0
((7 * -8 + 5x * -8) + 3x * (7 + 5x)) + -1(3x + -5)(5x + 4) = 0
((-56 + -40x) + 3x * (7 + 5x)) + -1(3x + -5)(5x + 4) = 0
(-56 + -40x + (7 * 3x + 5x * 3x)) + -1(3x + -5)(5x + 4) = 0
(-56 + -40x + (21x + 15x2)) + -1(3x + -5)(5x + 4) = 0

Combine like terms: -40x + 21x = -19x
(-56 + -19x + 15x2) + -1(3x + -5)(5x + 4) = 0

Reorder the terms:
-56 + -19x + 15x2 + -1(-5 + 3x)(5x + 4) = 0

Reorder the terms:
-56 + -19x + 15x2 + -1(-5 + 3x)(4 + 5x) = 0

Multiply (-5 + 3x) * (4 + 5x)
-56 + -19x + 15x2 + -1(-5(4 + 5x) + 3x * (4 + 5x)) = 0
-56 + -19x + 15x2 + -1((4 * -5 + 5x * -5) + 3x * (4 + 5x)) = 0
-56 + -19x + 15x2 + -1((-20 + -25x) + 3x * (4 + 5x)) = 0
-56 + -19x + 15x2 + -1(-20 + -25x + (4 * 3x + 5x * 3x)) = 0
-56 + -19x + 15x2 + -1(-20 + -25x + (12x + 15x2)) = 0

Combine like terms: -25x + 12x = -13x
-56 + -19x + 15x2 + -1(-20 + -13x + 15x2) = 0
-56 + -19x + 15x2 + (-20 * -1 + -13x * -1 + 15x2 * -1) = 0
-56 + -19x + 15x2 + (20 + 13x + -15x2) = 0

Reorder the terms:
-56 + 20 + -19x + 13x + 15x2 + -15x2 = 0

Combine like terms: -56 + 20 = -36
-36 + -19x + 13x + 15x2 + -15x2 = 0

Combine like terms: -19x + 13x = -6x
-36 + -6x + 15x2 + -15x2 = 0

Combine like terms: 15x2 + -15x2 = 0
-36 + -6x + 0 = 0
-36 + -6x = 0

Solving
-36 + -6x = 0

Solving for variable 'x'.

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

Add '36' to each side of the equation.
-36 + 36 + -6x = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -6x = 0 + 36
-6x = 0 + 36

Combine like terms: 0 + 36 = 36
-6x = 36

Divide each side by '-6'.
x = -6

Simplifying
x = -6

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