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

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


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

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

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

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

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

Add '3' to each side of the equation.
-3 + -10x + 3 + 8x2 = -3 + 3

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

Combine like terms: -3 + 3 = 0
0 + -10x + 8x2 = -3 + 3
-10x + 8x2 = -3 + 3

Combine like terms: -3 + 3 = 0
-10x + 8x2 = 0

Solving
-10x + 8x2 = 0

Solving for variable 'x'.

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

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, 1.25}

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