(4x-1)(2x+3)=15

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Solution for (4x-1)(2x+3)=15 equation: 


Simplifying
(4x + -1)(2x + 3) = 15

Reorder the terms:
(-1 + 4x)(2x + 3) = 15

Reorder the terms:
(-1 + 4x)(3 + 2x) = 15

Multiply (-1 + 4x) * (3 + 2x)
(-1(3 + 2x) + 4x * (3 + 2x)) = 15
((3 * -1 + 2x * -1) + 4x * (3 + 2x)) = 15
((-3 + -2x) + 4x * (3 + 2x)) = 15
(-3 + -2x + (3 * 4x + 2x * 4x)) = 15
(-3 + -2x + (12x + 8x2)) = 15

Combine like terms: -2x + 12x = 10x
(-3 + 10x + 8x2) = 15

Solving
-3 + 10x + 8x2 = 15

Solving for variable 'x'.

Reorder the terms:
-3 + -15 + 10x + 8x2 = 15 + -15

Combine like terms: -3 + -15 = -18
-18 + 10x + 8x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-18 + 10x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 5x + 4x2) = 0

Factor a trinomial.
2((-9 + -4x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-2.25, 1}

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