2x^2+5x-12=3x-8x^2

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Solution for 2x^2+5x-12=3x-8x^2 equation:


Simplifying
2x2 + 5x + -12 = 3x + -8x2

Reorder the terms:
-12 + 5x + 2x2 = 3x + -8x2

Solving
-12 + 5x + 2x2 = 3x + -8x2

Solving for variable 'x'.

Reorder the terms:
-12 + 5x + -3x + 2x2 + 8x2 = 3x + -8x2 + -3x + 8x2

Combine like terms: 5x + -3x = 2x
-12 + 2x + 2x2 + 8x2 = 3x + -8x2 + -3x + 8x2

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

Reorder the terms:
-12 + 2x + 10x2 = 3x + -3x + -8x2 + 8x2

Combine like terms: 3x + -3x = 0
-12 + 2x + 10x2 = 0 + -8x2 + 8x2
-12 + 2x + 10x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-12 + 2x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + x + 5x2) = 0

Factor a trinomial.
2((-6 + -5x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5x = 0 + 6
-5x = 0 + 6

Combine like terms: 0 + 6 = 6
-5x = 6

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2

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 = {-1.2, 1}

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