(5-2x)(2x+7)=4x^2-25

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Solution for (5-2x)(2x+7)=4x^2-25 equation: 


Simplifying
(5 + -2x)(2x + 7) = 4x2 + -25

Reorder the terms:
(5 + -2x)(7 + 2x) = 4x2 + -25

Multiply (5 + -2x) * (7 + 2x)
(5(7 + 2x) + -2x * (7 + 2x)) = 4x2 + -25
((7 * 5 + 2x * 5) + -2x * (7 + 2x)) = 4x2 + -25
((35 + 10x) + -2x * (7 + 2x)) = 4x2 + -25
(35 + 10x + (7 * -2x + 2x * -2x)) = 4x2 + -25
(35 + 10x + (-14x + -4x2)) = 4x2 + -25

Combine like terms: 10x + -14x = -4x
(35 + -4x + -4x2) = 4x2 + -25

Reorder the terms:
35 + -4x + -4x2 = -25 + 4x2

Solving
35 + -4x + -4x2 = -25 + 4x2

Solving for variable 'x'.

Reorder the terms:
35 + 25 + -4x + -4x2 + -4x2 = -25 + 4x2 + 25 + -4x2

Combine like terms: 35 + 25 = 60
60 + -4x + -4x2 + -4x2 = -25 + 4x2 + 25 + -4x2

Combine like terms: -4x2 + -4x2 = -8x2
60 + -4x + -8x2 = -25 + 4x2 + 25 + -4x2

Reorder the terms:
60 + -4x + -8x2 = -25 + 25 + 4x2 + -4x2

Combine like terms: -25 + 25 = 0
60 + -4x + -8x2 = 0 + 4x2 + -4x2
60 + -4x + -8x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
60 + -4x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + -1x + -2x2) = 0

Factor a trinomial.
4((5 + -2x)(3 + x)) = 0

Ignore the factor 4.

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {2.5, -3}

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