-3x(-4x+1)=-5x+10

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Solution for -3x(-4x+1)=-5x+10 equation: 


Simplifying
-3x(-4x + 1) = -5x + 10

Reorder the terms:
-3x(1 + -4x) = -5x + 10
(1 * -3x + -4x * -3x) = -5x + 10
(-3x + 12x2) = -5x + 10

Reorder the terms:
-3x + 12x2 = 10 + -5x

Solving
-3x + 12x2 = 10 + -5x

Solving for variable 'x'.

Reorder the terms:
-10 + -3x + 5x + 12x2 = 10 + -5x + -10 + 5x

Combine like terms: -3x + 5x = 2x
-10 + 2x + 12x2 = 10 + -5x + -10 + 5x

Reorder the terms:
-10 + 2x + 12x2 = 10 + -10 + -5x + 5x

Combine like terms: 10 + -10 = 0
-10 + 2x + 12x2 = 0 + -5x + 5x
-10 + 2x + 12x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-10 + 2x + 12x2 = 0

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

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

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

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

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {-1, 0.8333333333}

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