(2x-1)(x)=4x-7x+12

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Solution for (2x-1)(x)=4x-7x+12 equation: 


Simplifying
(2x + -1)(x) = 4x + -7x + 12

Reorder the terms:
(-1 + 2x)(x) = 4x + -7x + 12

Reorder the terms for easier multiplication:
x(-1 + 2x) = 4x + -7x + 12
(-1 * x + 2x * x) = 4x + -7x + 12
(-1x + 2x2) = 4x + -7x + 12

Reorder the terms:
-1x + 2x2 = 12 + 4x + -7x

Combine like terms: 4x + -7x = -3x
-1x + 2x2 = 12 + -3x

Solving
-1x + 2x2 = 12 + -3x

Solving for variable 'x'.

Reorder the terms:
-12 + -1x + 3x + 2x2 = 12 + -3x + -12 + 3x

Combine like terms: -1x + 3x = 2x
-12 + 2x + 2x2 = 12 + -3x + -12 + 3x

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

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

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

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

Factor a trinomial.
2((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}

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