(8x-3)(3x+2)-(4x+7)(x+4)=(2x+1)(5x-1)

Solution for (8x-3)(3x+2)-(4x+7)(x+4)=(2x+1)(5x-1) equation:

Simplifying
(8x + -3)(3x + 2) + -1(4x + 7)(x + 4) = (2x + 1)(5x + -1)

Reorder the terms:
(-3 + 8x)(3x + 2) + -1(4x + 7)(x + 4) = (2x + 1)(5x + -1)

Reorder the terms:
(-3 + 8x)(2 + 3x) + -1(4x + 7)(x + 4) = (2x + 1)(5x + -1)

Multiply (-3 + 8x) * (2 + 3x)
(-3(2 + 3x) + 8x * (2 + 3x)) + -1(4x + 7)(x + 4) = (2x + 1)(5x + -1)
((2 * -3 + 3x * -3) + 8x * (2 + 3x)) + -1(4x + 7)(x + 4) = (2x + 1)(5x + -1)
((-6 + -9x) + 8x * (2 + 3x)) + -1(4x + 7)(x + 4) = (2x + 1)(5x + -1)
(-6 + -9x + (2 * 8x + 3x * 8x)) + -1(4x + 7)(x + 4) = (2x + 1)(5x + -1)
(-6 + -9x + (16x + 24x2)) + -1(4x + 7)(x + 4) = (2x + 1)(5x + -1)

Combine like terms: -9x + 16x = 7x
(-6 + 7x + 24x2) + -1(4x + 7)(x + 4) = (2x + 1)(5x + -1)

Reorder the terms:
-6 + 7x + 24x2 + -1(7 + 4x)(x + 4) = (2x + 1)(5x + -1)

Reorder the terms:
-6 + 7x + 24x2 + -1(7 + 4x)(4 + x) = (2x + 1)(5x + -1)

Multiply (7 + 4x) * (4 + x)
-6 + 7x + 24x2 + -1(7(4 + x) + 4x * (4 + x)) = (2x + 1)(5x + -1)
-6 + 7x + 24x2 + -1((4 * 7 + x * 7) + 4x * (4 + x)) = (2x + 1)(5x + -1)
-6 + 7x + 24x2 + -1((28 + 7x) + 4x * (4 + x)) = (2x + 1)(5x + -1)
-6 + 7x + 24x2 + -1(28 + 7x + (4 * 4x + x * 4x)) = (2x + 1)(5x + -1)
-6 + 7x + 24x2 + -1(28 + 7x + (16x + 4x2)) = (2x + 1)(5x + -1)

Combine like terms: 7x + 16x = 23x
-6 + 7x + 24x2 + -1(28 + 23x + 4x2) = (2x + 1)(5x + -1)
-6 + 7x + 24x2 + (28 * -1 + 23x * -1 + 4x2 * -1) = (2x + 1)(5x + -1)
-6 + 7x + 24x2 + (-28 + -23x + -4x2) = (2x + 1)(5x + -1)

Reorder the terms:
-6 + -28 + 7x + -23x + 24x2 + -4x2 = (2x + 1)(5x + -1)

Combine like terms: -6 + -28 = -34
-34 + 7x + -23x + 24x2 + -4x2 = (2x + 1)(5x + -1)

Combine like terms: 7x + -23x = -16x
-34 + -16x + 24x2 + -4x2 = (2x + 1)(5x + -1)

Combine like terms: 24x2 + -4x2 = 20x2
-34 + -16x + 20x2 = (2x + 1)(5x + -1)

Reorder the terms:
-34 + -16x + 20x2 = (1 + 2x)(5x + -1)

Reorder the terms:
-34 + -16x + 20x2 = (1 + 2x)(-1 + 5x)

Multiply (1 + 2x) * (-1 + 5x)
-34 + -16x + 20x2 = (1(-1 + 5x) + 2x * (-1 + 5x))
-34 + -16x + 20x2 = ((-1 * 1 + 5x * 1) + 2x * (-1 + 5x))
-34 + -16x + 20x2 = ((-1 + 5x) + 2x * (-1 + 5x))
-34 + -16x + 20x2 = (-1 + 5x + (-1 * 2x + 5x * 2x))
-34 + -16x + 20x2 = (-1 + 5x + (-2x + 10x2))

Combine like terms: 5x + -2x = 3x
-34 + -16x + 20x2 = (-1 + 3x + 10x2)

Solving
-34 + -16x + 20x2 = -1 + 3x + 10x2

Solving for variable 'x'.

Reorder the terms:
-34 + 1 + -16x + -3x + 20x2 + -10x2 = -1 + 3x + 10x2 + 1 + -3x + -10x2

Combine like terms: -34 + 1 = -33
-33 + -16x + -3x + 20x2 + -10x2 = -1 + 3x + 10x2 + 1 + -3x + -10x2

Combine like terms: -16x + -3x = -19x
-33 + -19x + 20x2 + -10x2 = -1 + 3x + 10x2 + 1 + -3x + -10x2

Combine like terms: 20x2 + -10x2 = 10x2
-33 + -19x + 10x2 = -1 + 3x + 10x2 + 1 + -3x + -10x2

Reorder the terms:
-33 + -19x + 10x2 = -1 + 1 + 3x + -3x + 10x2 + -10x2

Combine like terms: -1 + 1 = 0
-33 + -19x + 10x2 = 0 + 3x + -3x + 10x2 + -10x2
-33 + -19x + 10x2 = 3x + -3x + 10x2 + -10x2

Combine like terms: 3x + -3x = 0
-33 + -19x + 10x2 = 0 + 10x2 + -10x2
-33 + -19x + 10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-33 + -19x + 10x2 = 0

Factor a trinomial.
(-11 + -10x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -10x)' equal to zero and attempt to solve:

Simplifying
-11 + -10x = 0

Solving
-11 + -10x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -10x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -10x = 0 + 11
-10x = 0 + 11

Combine like terms: 0 + 11 = 11
-10x = 11

Divide each side by '-10'.
x = -1.1

Simplifying
x = -1.1
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.1, 3}