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

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


Simplifying
(x + -4)(2x + 5) + -1(x + -4) = 0

Reorder the terms:
(-4 + x)(2x + 5) + -1(x + -4) = 0

Reorder the terms:
(-4 + x)(5 + 2x) + -1(x + -4) = 0

Multiply (-4 + x) * (5 + 2x)
(-4(5 + 2x) + x(5 + 2x)) + -1(x + -4) = 0
((5 * -4 + 2x * -4) + x(5 + 2x)) + -1(x + -4) = 0
((-20 + -8x) + x(5 + 2x)) + -1(x + -4) = 0
(-20 + -8x + (5 * x + 2x * x)) + -1(x + -4) = 0
(-20 + -8x + (5x + 2x2)) + -1(x + -4) = 0

Combine like terms: -8x + 5x = -3x
(-20 + -3x + 2x2) + -1(x + -4) = 0

Reorder the terms:
-20 + -3x + 2x2 + -1(-4 + x) = 0
-20 + -3x + 2x2 + (-4 * -1 + x * -1) = 0
-20 + -3x + 2x2 + (4 + -1x) = 0

Reorder the terms:
-20 + 4 + -3x + -1x + 2x2 = 0

Combine like terms: -20 + 4 = -16
-16 + -3x + -1x + 2x2 = 0

Combine like terms: -3x + -1x = -4x
-16 + -4x + 2x2 = 0

Solving
-16 + -4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2, 4}

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