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

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


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

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

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

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

Combine like terms: 10x + -8x = 2x
(-8 + 2x + 10x2) = 0

Solving
-8 + 2x + 10x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

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 '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

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

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

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

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-1, 0.8}

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