(4x+9)(14x-7)=0

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Solution for (4x+9)(14x-7)=0 equation: 


Simplifying
(4x + 9)(14x + -7) = 0

Reorder the terms:
(9 + 4x)(14x + -7) = 0

Reorder the terms:
(9 + 4x)(-7 + 14x) = 0

Multiply (9 + 4x) * (-7 + 14x)
(9(-7 + 14x) + 4x * (-7 + 14x)) = 0
((-7 * 9 + 14x * 9) + 4x * (-7 + 14x)) = 0
((-63 + 126x) + 4x * (-7 + 14x)) = 0
(-63 + 126x + (-7 * 4x + 14x * 4x)) = 0
(-63 + 126x + (-28x + 56x2)) = 0

Combine like terms: 126x + -28x = 98x
(-63 + 98x + 56x2) = 0

Solving
-63 + 98x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-9 + 14x + 8x2) = 0

Factor a trinomial.
7((-9 + -4x)(1 + -2x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x = 0 + 9
-4x = 0 + 9

Combine like terms: 0 + 9 = 9
-4x = 9

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

Subproblem 2
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
Solution
x = {-2.25, 0.5}

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