4x-5+(x+2)(8x-10)=0

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Solution for 4x-5+(x+2)(8x-10)=0 equation: 


Simplifying
4x + -5 + (x + 2)(8x + -10) = 0

Reorder the terms:
4x + -5 + (2 + x)(8x + -10) = 0

Reorder the terms:
4x + -5 + (2 + x)(-10 + 8x) = 0

Multiply (2 + x) * (-10 + 8x)
4x + -5 + (2(-10 + 8x) + x(-10 + 8x)) = 0
4x + -5 + ((-10 * 2 + 8x * 2) + x(-10 + 8x)) = 0
4x + -5 + ((-20 + 16x) + x(-10 + 8x)) = 0
4x + -5 + (-20 + 16x + (-10 * x + 8x * x)) = 0
4x + -5 + (-20 + 16x + (-10x + 8x2)) = 0

Combine like terms: 16x + -10x = 6x
4x + -5 + (-20 + 6x + 8x2) = 0

Reorder the terms:
-5 + -20 + 4x + 6x + 8x2 = 0

Combine like terms: -5 + -20 = -25
-25 + 4x + 6x + 8x2 = 0

Combine like terms: 4x + 6x = 10x
-25 + 10x + 8x2 = 0

Solving
-25 + 10x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -2x)(5 + -4x) = 0


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

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {-2.5, 1.25}

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