(2x+5)(2x-4)=400

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Solution for (2x+5)(2x-4)=400 equation: 


Simplifying
(2x + 5)(2x + -4) = 400

Reorder the terms:
(5 + 2x)(2x + -4) = 400

Reorder the terms:
(5 + 2x)(-4 + 2x) = 400

Multiply (5 + 2x) * (-4 + 2x)
(5(-4 + 2x) + 2x * (-4 + 2x)) = 400
((-4 * 5 + 2x * 5) + 2x * (-4 + 2x)) = 400
((-20 + 10x) + 2x * (-4 + 2x)) = 400
(-20 + 10x + (-4 * 2x + 2x * 2x)) = 400
(-20 + 10x + (-8x + 4x2)) = 400

Combine like terms: 10x + -8x = 2x
(-20 + 2x + 4x2) = 400

Solving
-20 + 2x + 4x2 = 400

Solving for variable 'x'.

Reorder the terms:
-20 + -400 + 2x + 4x2 = 400 + -400

Combine like terms: -20 + -400 = -420
-420 + 2x + 4x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-420 + 2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-210 + x + 2x2) = 0

Factor a trinomial.
2((-21 + -2x)(10 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + -2x)' equal to zero and attempt to solve:

Simplifying
-21 + -2x = 0

Solving
-21 + -2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -2x = 0 + 21
-2x = 0 + 21

Combine like terms: 0 + 21 = 21
-2x = 21

Divide each side by '-2'.
x = -10.5

Simplifying
x = -10.5

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-10.5, 10}

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