(2x-7)(x+2)-(x-8)(2x-3)=0

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Solution for (2x-7)(x+2)-(x-8)(2x-3)=0 equation: 


Simplifying
(2x + -7)(x + 2) + -1(x + -8)(2x + -3) = 0

Reorder the terms:
(-7 + 2x)(x + 2) + -1(x + -8)(2x + -3) = 0

Reorder the terms:
(-7 + 2x)(2 + x) + -1(x + -8)(2x + -3) = 0

Multiply (-7 + 2x) * (2 + x)
(-7(2 + x) + 2x * (2 + x)) + -1(x + -8)(2x + -3) = 0
((2 * -7 + x * -7) + 2x * (2 + x)) + -1(x + -8)(2x + -3) = 0
((-14 + -7x) + 2x * (2 + x)) + -1(x + -8)(2x + -3) = 0
(-14 + -7x + (2 * 2x + x * 2x)) + -1(x + -8)(2x + -3) = 0
(-14 + -7x + (4x + 2x2)) + -1(x + -8)(2x + -3) = 0

Combine like terms: -7x + 4x = -3x
(-14 + -3x + 2x2) + -1(x + -8)(2x + -3) = 0

Reorder the terms:
-14 + -3x + 2x2 + -1(-8 + x)(2x + -3) = 0

Reorder the terms:
-14 + -3x + 2x2 + -1(-8 + x)(-3 + 2x) = 0

Multiply (-8 + x) * (-3 + 2x)
-14 + -3x + 2x2 + -1(-8(-3 + 2x) + x(-3 + 2x)) = 0
-14 + -3x + 2x2 + -1((-3 * -8 + 2x * -8) + x(-3 + 2x)) = 0
-14 + -3x + 2x2 + -1((24 + -16x) + x(-3 + 2x)) = 0
-14 + -3x + 2x2 + -1(24 + -16x + (-3 * x + 2x * x)) = 0
-14 + -3x + 2x2 + -1(24 + -16x + (-3x + 2x2)) = 0

Combine like terms: -16x + -3x = -19x
-14 + -3x + 2x2 + -1(24 + -19x + 2x2) = 0
-14 + -3x + 2x2 + (24 * -1 + -19x * -1 + 2x2 * -1) = 0
-14 + -3x + 2x2 + (-24 + 19x + -2x2) = 0

Reorder the terms:
-14 + -24 + -3x + 19x + 2x2 + -2x2 = 0

Combine like terms: -14 + -24 = -38
-38 + -3x + 19x + 2x2 + -2x2 = 0

Combine like terms: -3x + 19x = 16x
-38 + 16x + 2x2 + -2x2 = 0

Combine like terms: 2x2 + -2x2 = 0
-38 + 16x + 0 = 0
-38 + 16x = 0

Solving
-38 + 16x = 0

Solving for variable 'x'.

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

Add '38' to each side of the equation.
-38 + 38 + 16x = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 16x = 0 + 38
16x = 0 + 38

Combine like terms: 0 + 38 = 38
16x = 38

Divide each side by '16'.
x = 2.375

Simplifying
x = 2.375

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