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

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


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

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

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

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

Combine like terms: -20x + 8x = -12x
(-20 + -12x + 8x2) = 0

Solving
-20 + -12x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -3x + 2x2) = 0

Factor a trinomial.
4((-1 + -1x)(5 + -2x)) = 0

Ignore the factor 4.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
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
Solution
x = {-1, 2.5}

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