(4x-5)(2x+3)=21

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Solution for (4x-5)(2x+3)=21 equation: 


Simplifying
(4x + -5)(2x + 3) = 21

Reorder the terms:
(-5 + 4x)(2x + 3) = 21

Reorder the terms:
(-5 + 4x)(3 + 2x) = 21

Multiply (-5 + 4x) * (3 + 2x)
(-5(3 + 2x) + 4x * (3 + 2x)) = 21
((3 * -5 + 2x * -5) + 4x * (3 + 2x)) = 21
((-15 + -10x) + 4x * (3 + 2x)) = 21
(-15 + -10x + (3 * 4x + 2x * 4x)) = 21
(-15 + -10x + (12x + 8x2)) = 21

Combine like terms: -10x + 12x = 2x
(-15 + 2x + 8x2) = 21

Solving
-15 + 2x + 8x2 = 21

Solving for variable 'x'.

Reorder the terms:
-15 + -21 + 2x + 8x2 = 21 + -21

Combine like terms: -15 + -21 = -36
-36 + 2x + 8x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-36 + 2x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + x + 4x2) = 0

Factor a trinomial.
2((-9 + -4x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4x = 0 + 9

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

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

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

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 = {-2.25, 2}

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