(2x+5)(2x-3)=9

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Solution for (2x+5)(2x-3)=9 equation:


Simplifying
(2x + 5)(2x + -3) = 9

Reorder the terms:
(5 + 2x)(2x + -3) = 9

Reorder the terms:
(5 + 2x)(-3 + 2x) = 9

Multiply (5 + 2x) * (-3 + 2x)
(5(-3 + 2x) + 2x * (-3 + 2x)) = 9
((-3 * 5 + 2x * 5) + 2x * (-3 + 2x)) = 9
((-15 + 10x) + 2x * (-3 + 2x)) = 9
(-15 + 10x + (-3 * 2x + 2x * 2x)) = 9
(-15 + 10x + (-6x + 4x2)) = 9

Combine like terms: 10x + -6x = 4x
(-15 + 4x + 4x2) = 9

Solving
-15 + 4x + 4x2 = 9

Solving for variable 'x'.

Reorder the terms:
-15 + -9 + 4x + 4x2 = 9 + -9

Combine like terms: -15 + -9 = -24
-24 + 4x + 4x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-24 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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