4(9-5x)(9-5x)=49

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Solution for 4(9-5x)(9-5x)=49 equation: 


Simplifying
4(9 + -5x)(9 + -5x) = 49

Multiply (9 + -5x) * (9 + -5x)
4(9(9 + -5x) + -5x * (9 + -5x)) = 49
4((9 * 9 + -5x * 9) + -5x * (9 + -5x)) = 49
4((81 + -45x) + -5x * (9 + -5x)) = 49
4(81 + -45x + (9 * -5x + -5x * -5x)) = 49
4(81 + -45x + (-45x + 25x2)) = 49

Combine like terms: -45x + -45x = -90x
4(81 + -90x + 25x2) = 49
(81 * 4 + -90x * 4 + 25x2 * 4) = 49
(324 + -360x + 100x2) = 49

Solving
324 + -360x + 100x2 = 49

Solving for variable 'x'.

Reorder the terms:
324 + -49 + -360x + 100x2 = 49 + -49

Combine like terms: 324 + -49 = 275
275 + -360x + 100x2 = 49 + -49

Combine like terms: 49 + -49 = 0
275 + -360x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(55 + -72x + 20x2) = 0

Factor a trinomial.
5((11 + -10x)(5 + -2x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(11 + -10x)' equal to zero and attempt to solve:

Simplifying
11 + -10x = 0

Solving
11 + -10x = 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 + -10x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -10x = 0 + -11
-10x = 0 + -11

Combine like terms: 0 + -11 = -11
-10x = -11

Divide each side by '-10'.
x = 1.1

Simplifying
x = 1.1

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1.1, 2.5}

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