12x^2-15x=8x-5

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Solution for 12x^2-15x=8x-5 equation: 


Simplifying
12x2 + -15x = 8x + -5

Reorder the terms:
-15x + 12x2 = 8x + -5

Reorder the terms:
-15x + 12x2 = -5 + 8x

Solving
-15x + 12x2 = -5 + 8x

Solving for variable 'x'.

Reorder the terms:
5 + -15x + -8x + 12x2 = -5 + 8x + 5 + -8x

Combine like terms: -15x + -8x = -23x
5 + -23x + 12x2 = -5 + 8x + 5 + -8x

Reorder the terms:
5 + -23x + 12x2 = -5 + 5 + 8x + -8x

Combine like terms: -5 + 5 = 0
5 + -23x + 12x2 = 0 + 8x + -8x
5 + -23x + 12x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
5 + -23x + 12x2 = 0

Factor a trinomial.
(1 + -4x)(5 + -3x) = 0


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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0.25, 1.666666667}

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