-7x(4x-1)+2=-28x+9

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Solution for -7x(4x-1)+2=-28x+9 equation: 


Simplifying
-7x(4x + -1) + 2 = -28x + 9

Reorder the terms:
-7x(-1 + 4x) + 2 = -28x + 9
(-1 * -7x + 4x * -7x) + 2 = -28x + 9
(7x + -28x2) + 2 = -28x + 9

Reorder the terms:
2 + 7x + -28x2 = -28x + 9

Reorder the terms:
2 + 7x + -28x2 = 9 + -28x

Solving
2 + 7x + -28x2 = 9 + -28x

Solving for variable 'x'.

Reorder the terms:
2 + -9 + 7x + 28x + -28x2 = 9 + -28x + -9 + 28x

Combine like terms: 2 + -9 = -7
-7 + 7x + 28x + -28x2 = 9 + -28x + -9 + 28x

Combine like terms: 7x + 28x = 35x
-7 + 35x + -28x2 = 9 + -28x + -9 + 28x

Reorder the terms:
-7 + 35x + -28x2 = 9 + -9 + -28x + 28x

Combine like terms: 9 + -9 = 0
-7 + 35x + -28x2 = 0 + -28x + 28x
-7 + 35x + -28x2 = -28x + 28x

Combine like terms: -28x + 28x = 0
-7 + 35x + -28x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-1 + 5x + -4x2) = 0

Factor a trinomial.
7((-1 + x)(1 + -4x)) = 0

Ignore the factor 7.

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, 0.25}

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