5(2x-5)=4x(2x+10)

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Solution for 5(2x-5)=4x(2x+10) equation:


Simplifying
5(2x + -5) = 4x(2x + 10)

Reorder the terms:
5(-5 + 2x) = 4x(2x + 10)
(-5 * 5 + 2x * 5) = 4x(2x + 10)
(-25 + 10x) = 4x(2x + 10)

Reorder the terms:
-25 + 10x = 4x(10 + 2x)
-25 + 10x = (10 * 4x + 2x * 4x)
-25 + 10x = (40x + 8x2)

Solving
-25 + 10x = 40x + 8x2

Solving for variable 'x'.

Combine like terms: 10x + -40x = -30x
-25 + -30x + -8x2 = 40x + 8x2 + -40x + -8x2

Reorder the terms:
-25 + -30x + -8x2 = 40x + -40x + 8x2 + -8x2

Combine like terms: 40x + -40x = 0
-25 + -30x + -8x2 = 0 + 8x2 + -8x2
-25 + -30x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-25 + -30x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25 + 30x + 8x2) = 0

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

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

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

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

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

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {-2.5, -1.25}

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