(4x+10)(2x-4)=180

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Solution for (4x+10)(2x-4)=180 equation: 


Simplifying
(4x + 10)(2x + -4) = 180

Reorder the terms:
(10 + 4x)(2x + -4) = 180

Reorder the terms:
(10 + 4x)(-4 + 2x) = 180

Multiply (10 + 4x) * (-4 + 2x)
(10(-4 + 2x) + 4x * (-4 + 2x)) = 180
((-4 * 10 + 2x * 10) + 4x * (-4 + 2x)) = 180
((-40 + 20x) + 4x * (-4 + 2x)) = 180
(-40 + 20x + (-4 * 4x + 2x * 4x)) = 180
(-40 + 20x + (-16x + 8x2)) = 180

Combine like terms: 20x + -16x = 4x
(-40 + 4x + 8x2) = 180

Solving
-40 + 4x + 8x2 = 180

Solving for variable 'x'.

Reorder the terms:
-40 + -180 + 4x + 8x2 = 180 + -180

Combine like terms: -40 + -180 = -220
-220 + 4x + 8x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-220 + 4x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-55 + x + 2x2) = 0

Factor a trinomial.
4((-11 + -2x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-11 + -2x)' equal to zero and attempt to solve:

Simplifying
-11 + -2x = 0

Solving
-11 + -2x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x = 0 + 11
-2x = 0 + 11

Combine like terms: 0 + 11 = 11
-2x = 11

Divide each side by '-2'.
x = -5.5

Simplifying
x = -5.5

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-5.5, 5}

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