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

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Solution for =(3x+1)(x-5)-(x-5)(7x+4) equation: 


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

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

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

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

Combine like terms: 1x + -15x = -14x
0 = (-5 + -14x + 3x2) + -1(x + -5)(7x + 4)

Reorder the terms:
0 = -5 + -14x + 3x2 + -1(-5 + x)(7x + 4)

Reorder the terms:
0 = -5 + -14x + 3x2 + -1(-5 + x)(4 + 7x)

Multiply (-5 + x) * (4 + 7x)
0 = -5 + -14x + 3x2 + -1(-5(4 + 7x) + x(4 + 7x))
0 = -5 + -14x + 3x2 + -1((4 * -5 + 7x * -5) + x(4 + 7x))
0 = -5 + -14x + 3x2 + -1((-20 + -35x) + x(4 + 7x))
0 = -5 + -14x + 3x2 + -1(-20 + -35x + (4 * x + 7x * x))
0 = -5 + -14x + 3x2 + -1(-20 + -35x + (4x + 7x2))

Combine like terms: -35x + 4x = -31x
0 = -5 + -14x + 3x2 + -1(-20 + -31x + 7x2)
0 = -5 + -14x + 3x2 + (-20 * -1 + -31x * -1 + 7x2 * -1)
0 = -5 + -14x + 3x2 + (20 + 31x + -7x2)

Reorder the terms:
0 = -5 + 20 + -14x + 31x + 3x2 + -7x2

Combine like terms: -5 + 20 = 15
0 = 15 + -14x + 31x + 3x2 + -7x2

Combine like terms: -14x + 31x = 17x
0 = 15 + 17x + 3x2 + -7x2

Combine like terms: 3x2 + -7x2 = -4x2
0 = 15 + 17x + -4x2

Solving
0 = 15 + 17x + -4x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + -17x + 4x2 = 15 + 17x + -4x2 + -15 + -17x + 4x2

Reorder the terms:
-15 + -17x + 4x2 = 15 + -15 + 17x + -17x + -4x2 + 4x2

Combine like terms: 15 + -15 = 0
-15 + -17x + 4x2 = 0 + 17x + -17x + -4x2 + 4x2
-15 + -17x + 4x2 = 17x + -17x + -4x2 + 4x2

Combine like terms: 17x + -17x = 0
-15 + -17x + 4x2 = 0 + -4x2 + 4x2
-15 + -17x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-15 + -17x + 4x2 = 0

Factor a trinomial.
(-3 + -4x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.75, 5}

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