12x^2+15x=16x+20

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Solution for 12x^2+15x=16x+20 equation: 


Simplifying
12x2 + 15x = 16x + 20

Reorder the terms:
15x + 12x2 = 16x + 20

Reorder the terms:
15x + 12x2 = 20 + 16x

Solving
15x + 12x2 = 20 + 16x

Solving for variable 'x'.

Reorder the terms:
-20 + 15x + -16x + 12x2 = 20 + 16x + -20 + -16x

Combine like terms: 15x + -16x = -1x
-20 + -1x + 12x2 = 20 + 16x + -20 + -16x

Reorder the terms:
-20 + -1x + 12x2 = 20 + -20 + 16x + -16x

Combine like terms: 20 + -20 = 0
-20 + -1x + 12x2 = 0 + 16x + -16x
-20 + -1x + 12x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
-20 + -1x + 12x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-1.25, 1.333333333}

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