(9x-7)(4x+2)=0

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Solution for (9x-7)(4x+2)=0 equation: 


Simplifying
(9x + -7)(4x + 2) = 0

Reorder the terms:
(-7 + 9x)(4x + 2) = 0

Reorder the terms:
(-7 + 9x)(2 + 4x) = 0

Multiply (-7 + 9x) * (2 + 4x)
(-7(2 + 4x) + 9x * (2 + 4x)) = 0
((2 * -7 + 4x * -7) + 9x * (2 + 4x)) = 0
((-14 + -28x) + 9x * (2 + 4x)) = 0
(-14 + -28x + (2 * 9x + 4x * 9x)) = 0
(-14 + -28x + (18x + 36x2)) = 0

Combine like terms: -28x + 18x = -10x
(-14 + -10x + 36x2) = 0

Solving
-14 + -10x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -5x + 18x2) = 0

Factor a trinomial.
2((-1 + -2x)(7 + -9x)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(7 + -9x)' equal to zero and attempt to solve:

Simplifying
7 + -9x = 0

Solving
7 + -9x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -9x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9x = 0 + -7
-9x = 0 + -7

Combine like terms: 0 + -7 = -7
-9x = -7

Divide each side by '-9'.
x = 0.7777777778

Simplifying
x = 0.7777777778
Solution
x = {-0.5, 0.7777777778}

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