(7x+2)(2x-3)=5x-6

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Solution for (7x+2)(2x-3)=5x-6 equation: 


Simplifying
(7x + 2)(2x + -3) = 5x + -6

Reorder the terms:
(2 + 7x)(2x + -3) = 5x + -6

Reorder the terms:
(2 + 7x)(-3 + 2x) = 5x + -6

Multiply (2 + 7x) * (-3 + 2x)
(2(-3 + 2x) + 7x * (-3 + 2x)) = 5x + -6
((-3 * 2 + 2x * 2) + 7x * (-3 + 2x)) = 5x + -6
((-6 + 4x) + 7x * (-3 + 2x)) = 5x + -6
(-6 + 4x + (-3 * 7x + 2x * 7x)) = 5x + -6
(-6 + 4x + (-21x + 14x2)) = 5x + -6

Combine like terms: 4x + -21x = -17x
(-6 + -17x + 14x2) = 5x + -6

Reorder the terms:
-6 + -17x + 14x2 = -6 + 5x

Add '6' to each side of the equation.
-6 + -17x + 6 + 14x2 = -6 + 6 + 5x

Reorder the terms:
-6 + 6 + -17x + 14x2 = -6 + 6 + 5x

Combine like terms: -6 + 6 = 0
0 + -17x + 14x2 = -6 + 6 + 5x
-17x + 14x2 = -6 + 6 + 5x

Combine like terms: -6 + 6 = 0
-17x + 14x2 = 0 + 5x
-17x + 14x2 = 5x

Solving
-17x + 14x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-17x + -5x + 14x2 = 5x + -5x

Combine like terms: -17x + -5x = -22x
-22x + 14x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-22x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-11 + 7x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-11 + 7x)' equal to zero and attempt to solve:

Simplifying
-11 + 7x = 0

Solving
-11 + 7x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 7x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 7x = 0 + 11
7x = 0 + 11

Combine like terms: 0 + 11 = 11
7x = 11

Divide each side by '7'.
x = 1.571428571

Simplifying
x = 1.571428571
Solution
x = {0, 1.571428571}

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